LAWS OF MOTION MCQs for JEE PHYSICS — Easy

1 Easy

1 of 34

Understanding +4 | -1

You are pushing a wooden crate across the floor at a constant speed. You decide to change the orientation of crate such that area of contact with floor become half. In the new orientation, to push the same crate across the same floor with the same constant speed, the force that you apply must be about as the force required before you changed the crate's orientation.

View answer and explanation

Correct option: C

Equally great

Option C (Equally great) is correct because the force required to push the crate at a constant speed depends on the kinetic friction, which is independent of the area of contact.

Solution approach

Correct Answer + Core Reason: Equally great. Kinetic friction is independent of the area of contact.

Step-by-Step Solution:

Step 1: Recall the formula for kinetic friction: $f_k = \mu_k N$ , where $\mu_k$ is the coefficient of kinetic friction and $N$ is the normal force.

Step 2: Note that the normal force is equal to the weight of the crate, which remains constant regardless of the orientation.

Step 3: Since the coefficient of kinetic friction and the normal force remain the same, the kinetic friction remains the same.

Step 4: To push the crate at a constant speed, the applied force must be equal to the kinetic friction. Therefore, the applied force remains the same.

Why other options are wrong:
- Option A: 4 times as great is incorrect because the friction does not depend on the area of contact.
- Option B: 2 times as great is incorrect because the friction does not depend on the area of contact.
- Option D: $1 / 2$ as great is incorrect because the friction does not depend on the area of contact.

Key Concepts:
- Kinetic friction
- Normal force
- Coefficient of kinetic friction

Memory Aids:
- Remember that kinetic friction is independent of the area of contact.

Quick Tips:
- The force required to maintain constant speed is equal to the friction force.

2 Easy

2 of 34

Application +4 | -1

A body of mass M collides against a wall with a velocity V and retraces its path with the same speed. The change in momentum is [take initial direction of velocity as positive]

View answer and explanation

Correct option: D

- 2 MV

Option D (- 2 MV) is correct because the change in momentum is the final momentum minus the initial momentum, considering the direction change.

Solution approach

Correct Answer + Core Reason: - 2 MV. The change in momentum is calculated considering the change in direction.

Step-by-Step Solution:

Step 1: Define the initial momentum: $p_1 = MV$ .

Step 2: Define the final momentum: $p_2 = -MV$ (since the object retraces its path with the same speed).

Step 3: Calculate the change in momentum: $\Delta p = p_2 - p_1 = -MV - MV$ .

Step 4: Simplify the expression: $\Delta p = -2MV$ .

Final Answer: - 2 MV

Why other options are wrong:
- Option A (Zero): This is incorrect because it assumes the momentum is unchanged, neglecting the change in direction.
- Option B (2 MV): This is incorrect because it calculates the sum of the initial and final momentum instead of the difference.
- Option C (MV): This is incorrect because it only considers the initial or final momentum, not the change.

Key Concepts:
- Momentum
- Change in momentum
- Vector quantities

Memory Aids:
- $\Delta p = p_f - p_i$ (Change in momentum equals final momentum minus initial momentum)

Quick Tips:
- Remember that momentum is a vector quantity and direction is important.
- Pay attention to the sign conventions when calculating changes in momentum.

3 Easy

3 of 34

Analyzing +4 | -1

If a coin is dropped in a lift it takes

t_1

time to reach the floor and takes

t_2

time when lift is moving up with constant acceleration, then which one of the following relation is correct?

View answer and explanation

Correct option: B

t_1>t_2

Option B (

t_1>t_2

) is correct because when the lift moves upwards with constant acceleration, the effective acceleration increases, thus reducing the time taken for the coin to reach the floor.

Solution approach

Correct Answer + Core Reason: $t_1>t_2$ . The effective acceleration is greater when the lift is accelerating upwards.

Step-by-Step Solution:

Step 1: Define the variables: Let $h$ be the height of the lift, $g$ be the acceleration due to gravity, and $a$ be the upward acceleration of the lift.

Step 2: Time taken when the lift is stationary: $t_1 = \sqrt{\frac{{2h}}{{g}}}$

Step 3: Time taken when the lift is moving upwards with constant acceleration: The effective acceleration is $g+a$ . Therefore, $t_2 = \sqrt{\frac{{2h}}{{g+a}}}$

Step 4: Compare $t_1$ and $t_2$ : Since $g+a > g$ , we have $\sqrt{\frac{{2h}}{{g+a}}} < \sqrt{\frac{{2h}}{{g}}}$ . Therefore, $t_2 < t_1$ .

Step 5: Final Answer: $t_1 > t_2$

Why other options are wrong:
- Option A: $t_1=t_2$ is incorrect because the acceleration changes when the lift accelerates.
- Option C: $t_2>t_1$ is incorrect because the time taken is less when the acceleration is greater.
- Option D: $t_1 \gg t_2$ is incorrect because the difference in time is not significantly large; it depends on the value of 'a'.

Key Concepts:
- Kinematics
- Acceleration due to gravity
- Effective acceleration

Memory Aids:
- When the lift accelerates upwards, the apparent weight increases.

Quick Tips:
- Remember to consider the effective acceleration when dealing with non-inertial frames of reference.

4 Easy

4 of 34

Application +4 | -1

A vehicle of mass 125 kg is moving with a velocity of 90 kmph. What force should be applied on the vehicle to stop it in 5 s

View answer and explanation

Correct option: D

625 N

Option D (625 N) is correct because the force required to stop the vehicle is calculated using Newton's second law,

F = ma

, where

a

is the deceleration.

Solution approach

Correct Answer + Core Reason: 625 N. The force is calculated using Newton's second law.

Step-by-Step Solution:

Step 1: Identify the given values: $m = 125 \mathrm{~kg}$ , $u = 90 \mathrm{~km/h} = 25 \mathrm{~m/s}$ , $v = 0 \mathrm{~m/s}$ , $t = 5 \mathrm{~s}$ .

Step 2: Calculate the acceleration: $a = \frac{v - u}{t} = \frac{0 - 25}{5} = -5 \mathrm{~m/s^2}$ .

Step 3: Calculate the force: $F = ma = 125 \times (-5) = -625 \mathrm{~N}$ . The magnitude of the force is 625 N.

Step 4: Final Answer: 625 N

Why other options are wrong:
- Option A: Incorrect calculation of acceleration or force.
- Option B: Incorrect calculation of acceleration or force.
- Option C: Incorrect calculation of acceleration or force.

Key Concepts:
- Newton's Second Law
- Kinematics

Memory Aids:
- $F = ma$ (Force equals mass times acceleration)
- $v = u + at$ (Kinematic equation)

Quick Tips:
- Convert all units to SI units before calculation.

5 Easy

5 of 34

Application +4 | -1

A person wants to drive on the vertical surface of a large cylindrical wooden 'well' commonly known as 'death well' in a circus. The radius of the well is

\mathrm{R}

and the coefficient of friction between the tyres of the motorcycle and the wall of the well is

\mu_{\mathrm{s}}

. The minimum speed the motor cyclist must have in order to prevent slipping should be

View answer and explanation

Correct option: A

\sqrt{\frac{g \mathrm{R}}{\mu_{\mathrm{s}}}}

Option A (

\sqrt{\frac{g \mathrm{R}}{\mu_{\mathrm{s}}}}

) is correct because it represents the minimum speed required to prevent slipping, derived from balancing the gravitational force and frictional force.

Solution approach

Correct Answer + Core Reason: $\sqrt{\frac{g \mathrm{R}}{\mu_{\mathrm{s}}}}$ . The minimum speed is derived from balancing the normal force with the centripetal force and the frictional force with the gravitational force.

Step-by-Step Solution:

Step 1: Draw a free-body diagram of the motorcycle on the wall.

Step 2: Identify the forces acting on the motorcycle: weight ( $mg$ ) downwards, normal force ( $N$ ) towards the center of the circle, and friction force ( $f$ ) upwards.

Step 3: Write the equation for the normal force in terms of centripetal force: $N = \frac{mv^2}{R}$ .

Step 4: Write the equation for the friction force: $f = \mu_s N$ .

Step 5: For the motorcycle not to slip, the friction force must balance the weight: $f = mg$ .

Step 6: Substitute $f = \mu_s N$ into $f = mg$ : $\mu_s N = mg$ .

Step 7: Substitute $N = \frac{mv^2}{R}$ into $\mu_s N = mg$ : $\mu_s \frac{mv^2}{R} = mg$ .

Step 8: Solve for $v$ : $v^2 = \frac{gR}{\mu_s}$ , so $v = \sqrt{\frac{gR}{\mu_s}}$ .

Why other options are wrong:
- **Option B ( $\sqrt{\frac{\mu_s}{\mathrm{gR}}}$ ): This is incorrect because it inverts the relationship between the speed and the coefficient of friction.
- Option C ( $\sqrt{\frac{\mu_s g}{R}}$ ): This is incorrect because it has the coefficient of friction in the numerator instead of the denominator.
- Option D ( $\sqrt{\frac{\mathrm{R}}{\mu_{\mathrm{s}} g}}$ ): This is incorrect because it has the acceleration due to gravity in the denominator instead of the numerator.

Key Concepts:**
- Centripetal Force: $F_c = \frac{mv^2}{R}$
- Friction Force: $f = \mu N$
- Newton's Laws of Motion

Memory Aids:
- Remember that the friction force opposes the direction of potential motion.

Quick Tips:
- Always draw a free-body diagram to visualize the forces acting on the object.
- Ensure that the units are consistent throughout the calculation.

6 Easy

6 of 34

Application +4 | -1

A bullet of mass 28 gm is fired from a rifle of mass 10 kg with a velocity of 100 m/s. The velocity of recoil of the rifle is

View answer and explanation

Correct option: A

-0.28

Option A (-0.28) is correct because it is calculated using the conservation of momentum, where the total momentum before firing equals the total momentum after firing.

Solution approach

Correct Answer + Core Reason: -0.28. The recoil velocity is calculated using conservation of momentum.

Step-by-Step Solution:

Step 1: Identify the given information: $m_b = 0.028 \text{{ kg}}$ , $v_b = 100 \text{{ m/s}}$ , $m_g = 10 \text{{ kg}}$ .

Step 2: Apply the conservation of momentum: $m_b v_b + m_g v_g = 0$ (initial momentum is zero).

Step 3: Substitute the given values: $(0.028 \text{{ kg}})(100 \text{{ m/s}}) + (10 \text{{ kg}})v_g = 0$ .

Step 4: Solve for $v_g$ : $2.8 + 10v_g = 0$ , so $v_g = -\frac{{2.8}}{{10}} = -0.28 \text{{ m/s}}$ .

Why other options are wrong:
- Option B (1.28): This is likely a calculation error or incorrect application of the conservation of momentum.
- Option C (-1.28): This is also likely a calculation error, possibly misplacing the decimal point.
- Option D (0.56): This is a calculation error; the correct recoil velocity is -0.28 m/s.

Key Concepts:
- Conservation of Momentum: $m_1v_1 + m_2v_2 = constant$

Memory Aids:
- Remember that recoil velocity is in the opposite direction to the bullet's velocity.

Quick Tips:
- Always convert masses to kg and velocities to m/s before calculations.
- Pay attention to the direction of velocities (use negative sign for recoil).

7 Easy

7 of 34

Analyzing +4 | -1

Three forces are acting on a body to make it in equilibrium, which set can not do it?

View answer and explanation

Correct option: A

3 {~N}, 3 {~N}, 7 {~N}

Option A (

3 {~N}, 3 {~N}, 7 {~N}

) is correct because these forces cannot form a closed triangle, violating the condition for equilibrium.

Solution approach

Correct Answer + Core Reason: $3 {~N}, 3 {~N}, 7 {~N}$ . For equilibrium, the sum of any two forces must be greater than or equal to the third force (triangle inequality).

Step-by-Step Solution:

Step 1: Check the triangle inequality for each set of forces.

Step 2: For option A: $3 + 3 = 6 < 7$ . This set does not satisfy the triangle inequality.

Step 3: For option B: $2 + 3 = 5 > 4$ , $2 + 4 = 6 > 3$ , $3 + 4 = 7 > 2$ . This set satisfies the triangle inequality.

Step 4: For option C: $2 + 1 = 3 > 1$ , $1 + 1 = 2 \geq 2$ . This set satisfies the triangle inequality.

Step 5: For option D: $8 + 6 = 14 > 4$ , $8 + 4 = 12 > 6$ , $6 + 4 = 10 > 8$ . This set satisfies the triangle inequality.

Why other options are wrong:
- Option B: $2 {~N}, 3 {~N}, 4 {~N}$ can form a triangle and thus be in equilibrium.
- Option C: $2 {~N}, 1 {~N}, 1 {~N}$ can form a triangle and thus be in equilibrium.
- Option D: $8 {~N}, 6 {~N}, 4 {~N}$ can form a triangle and thus be in equilibrium.

Key Concepts:
- Equilibrium of Forces
- Triangle Inequality

Memory Aids:
- Remember that for three forces to be in equilibrium, they must be able to form a closed triangle.

Quick Tips:
- Check the triangle inequality for each set of forces to determine if they can be in equilibrium.

8 Easy

8 of 34

Application +4 | -1

On the horizontal surface of a truck

\left( {\mu = 0.6} \right)

, a block of mass 1 kg is placed. If the truck is accelerating at the rate of

5m/se{c^2}

then frictional force on the block will be

View answer and explanation

Correct option: A

5 N

Option A (5 N) is correct because the frictional force on the block is 5 N, which is equal to the pseudo force acting on it since the pseudo force is less than the limiting friction.

Solution approach

Correct Answer + Core Reason: 5 N. The frictional force equals the pseudo force since it's less than limiting friction.

Step-by-Step Solution:

Step 1: Calculate the limiting friction: ${F_l} = \mu mg = 0.6 \times 1 \times 9.8 = 5.88 \text{{ N}}$ .

Step 2: Calculate the pseudo force on the block: $F_{pseudo} = ma = 1 \times 5 = 5 \text{{ N}}$ .

Step 3: Since the pseudo force is less than the limiting friction ( $5 \text{{ N}} < 5.88 \text{{ N}}$ ), the static friction force is equal to the pseudo force.

Step 4: Therefore, the frictional force on the block is 5 N.

Why other options are wrong:
- Option B: Incorrect, this is greater than the pseudo force and not equal to the limiting friction.
- Option C: Incorrect, this is the limiting friction, but the actual friction is less because the pseudo force is less than the limiting friction.
- Option D: Incorrect, this is not related to the frictional force or the pseudo force.

Key Concepts:
- Friction
- Pseudo force

Memory Aids:
- Remember that static friction adjusts to match the applied force, up to the limiting friction.

Quick Tips:
- Compare the pseudo force with the limiting friction to determine the actual friction force.

9 Easy

9 of 34

Understanding +4 | -1

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

View answer and explanation

Correct option: A

To conduct excess charge due to air friction to ground and prevent sparking

The correct answer is A because the metallic chains conduct static electricity generated by friction to the ground, preventing sparks that could ignite the inflammable fluids.

Solution approach

Correct Answer + Core Reason: To conduct excess charge due to air friction to ground and prevent sparking. This prevents static electricity buildup.

Step-by-Step Solution:
Step 1: Identify the source of charge: As vehicles move, friction between the vehicle and the air can cause a buildup of static electric charge on the vehicle.
Step 2: Explain the purpose of the chains: The metallic chains provide a conductive path for the static charge to flow from the vehicle to the ground.
Step 3: Explain the prevention of sparking: By discharging the static charge to the ground, the chains prevent the buildup of charge to a level where it could cause a spark, which could ignite the inflammable fluids.

Why other options are wrong:
- Option B: To alert other vehicles: Incorrect because the chains are not primarily for alerting other vehicles.
- Option C: To protect tyres from catching dirt from ground: Incorrect because the chains are not primarily for protecting the tires.
- Option D: It is a custom: Incorrect because there is a scientific reason for the chains.

Key Concepts:
- Static Electricity
- Conduction
- Grounding

Memory Aids:
- Chains ground the vehicle, preventing sparks.

Quick Tips:
- Remember that static electricity can be dangerous in the presence of flammable materials.

10 Easy

10 of 34

Analyzing +4 | -1

An electric fan is placed on a stationary boat
and air is blown with it on the sail of the boat.
Which of the following statements is correct?

View answer and explanation

Correct option: D

The boat will remain stationary as before

Option D is correct. The boat will remain stationary because the force exerted by the fan on the air is equal and opposite to the force exerted by the air on the sail, resulting in a net force of zero on the boat.

Solution approach

Correct Answer + Core Reason: The boat will remain stationary as before. The net force on the boat is zero due to Newton's third law.

Step-by-Step Solution:

Step 1: Analyze the forces acting on the boat.

Step 2: The electric fan blows air on the sail. The fan exerts a force on the air, and by Newton's third law, the air exerts an equal and opposite force on the fan.

Step 3: Since the fan is attached to the boat, this force is transmitted to the boat in the opposite direction of the airflow.

Step 4: The air then exerts a force on the sail in the direction of the airflow.

Step 5: The net force on the boat is the sum of the force exerted by the fan on the boat and the force exerted by the air on the sail. These forces are equal in magnitude and opposite in direction, so the net force is zero.

Step 6: Therefore, the boat will remain stationary.

Why other options are wrong:
- Option A: The boat will not be uniformly accelerated because the net force is zero.
- Option B: The boat will not start moving with uniform speed because the net force is zero.
- Option C: The boat will not be uniformly accelerated in the opposite direction because the net force is zero.

Key Concepts:
- Newton's Third Law of Motion
- Action-Reaction Forces

Memory Aids:
- For every action, there is an equal and opposite reaction.

Quick Tips:
- Consider all forces acting on the system.

11 Easy

11 of 34

Understanding +4 | -1

Which one of the following is not a contact force?

View answer and explanation

Correct option: D

Magnetic force

Option D (Magnetic force) is correct because magnetic force is a non-contact force, acting through a field.

Solution approach

Correct Answer + Core Reason: Magnetic force. It is a non-contact force.

Step-by-Step Solution:

Step 1: Define contact force.

Step 2: Key Concept: A contact force requires physical contact between two objects.

Step 3: Analyze the options:
- Viscous force: Requires contact (fluid and object).
- Air resistance: Requires contact (air and object).
- Friction: Requires contact (two surfaces).
- Magnetic force: Acts through a field, no direct contact needed.

Why other options are wrong:
- Option A: Incorrect because viscous force is a contact force.
- Option B: Incorrect because air resistance is a contact force.
- Option C: Incorrect because friction is a contact force.

Key Concepts:
- Contact force
- Non-contact force
- Magnetic force
- Viscous force
- Friction
- Air resistance

Memory Aids:
- Contact = Touch

Quick Tips:
- Remember that forces acting through fields (gravity, electromagnetism) are non-contact forces.

12 Easy

12 of 34

Application +4 | -1

The coefficients of static and dynamic friction are 0.7 and 0.4. The minimum force required to create motion is applied on a body and if it is further continued, the acceleration attained by the body in

m{s^{ - 2}}

is

(g = 10\,m/{s^2})

View answer and explanation

Correct option: C

3

Option C (3) is correct because the acceleration is calculated as the difference between the static and dynamic friction coefficients multiplied by the acceleration due to gravity.

Solution approach

Correct Answer + Core Reason: 3. The acceleration is calculated using the difference between the static and kinetic friction coefficients.

Step-by-Step Solution:

Step 1: Identify the given information: coefficient of static friction $\mu_s = 0.7$ , coefficient of dynamic friction $\mu_k = 0.4$ , and acceleration due to gravity $g = 10 \text{{ m/s}}^2$ .

Step 2: The net force causing acceleration is related to the difference between the static and kinetic friction. The formula for acceleration is $a = (\mu_s - \mu_k)g$ only applies if the applied force is *just enough* to overcome static friction. In this case, it's implied that the force is only infinitesimally larger than the static friction force.

Step 3: Substitute the values: $a = (0.7 - 0.4) \times 10$ .

Step 4: Calculate the acceleration: $a = 0.3 \times 10 = 3 \text{{ m/s}}^2$ .

Why other options are wrong:
- Option A (7): This is incorrect because it only considers the static friction coefficient and ignores the dynamic friction.
- Option B (4): This is incorrect because it only considers the dynamic friction coefficient and ignores the static friction.
- Option D (Zero): This is incorrect because once the body starts moving, the kinetic friction comes into play, resulting in a non-zero acceleration.

Key Concepts:
- Static Friction
- Kinetic Friction
- Newton's Second Law of Motion

Memory Aids:
- Static friction prevents motion, while kinetic friction opposes motion.
- Remember that kinetic friction is generally less than static friction.

Quick Tips:
- Always distinguish between static and kinetic friction.
- The acceleration depends on the net force, which is the difference between the applied force and the friction force.

13 Easy

13 of 34

Application +4 | -1

The coefficients of static and dynamic friction are 0.7 and 0.4. The minimum force required to create motion is applied on a body and if it is further continued, the acceleration attained by the body in

m{s^{ - 2}}

is

(g = 10\,m/{s^2})

View answer and explanation

Correct option: C

3

Option C (3) is correct because the acceleration is calculated as the difference between the static and dynamic friction coefficients multiplied by the acceleration due to gravity.

Solution approach

Correct Answer + Core Reason: 3. The acceleration is calculated using the difference between the static and kinetic friction coefficients.

Step-by-Step Solution:

Step 1: Identify the given information: coefficient of static friction $\mu_s = 0.7$ , coefficient of dynamic friction $\mu_k = 0.4$ , and acceleration due to gravity $g = 10 \text{{ m/s}}^2$ .

Step 2: The net force causing acceleration is related to the difference between the static and kinetic friction. The formula for acceleration is $a = (\mu_s - \mu_k)g$ only applies if the applied force is *just enough* to overcome static friction. In this case, it's implied that the force is only infinitesimally larger than the static friction force.

Step 3: Substitute the values: $a = (0.7 - 0.4) \times 10$ .

Step 4: Calculate the acceleration: $a = 0.3 \times 10 = 3 \text{{ m/s}}^2$ .

Why other options are wrong:
- Option A (7): This is incorrect because it only considers the static friction coefficient and ignores the dynamic friction.
- Option B (4): This is incorrect because it only considers the dynamic friction coefficient and ignores the static friction.
- Option D (Zero): This is incorrect because once the body starts moving, the kinetic friction comes into play, resulting in a non-zero acceleration.

Key Concepts:
- Static Friction
- Kinetic Friction
- Newton's Second Law of Motion

Memory Aids:
- Static friction prevents motion, while kinetic friction opposes motion.
- Remember that kinetic friction is generally less than static friction.

Quick Tips:
- Always distinguish between static and kinetic friction.
- The acceleration depends on the net force, which is the difference between the applied force and the friction force.

14 Easy

14 of 34

Application +4 | -1

A stationary particle breaks into two parts of masses

\mathrm{m}_{\mathrm{A}}

and

\mathrm{m}_{\mathrm{B}}

which move with velocities

\mathrm{v}_{\mathrm{A}}

and

\mathrm{v}_{\mathrm{B}}

respectively. The ratio of their kinetic energies

\left(\mathrm{K}_{\mathrm{B}}: \mathrm{K}_{\mathrm{A}}\right)

is :

View answer and explanation

Correct option: A

\mathrm{v}_{\mathrm{B}}: \mathrm{v}_{\mathrm{A}}

Option A (

\mathrm{v}_{\mathrm{B}}: \mathrm{v}_{\mathrm{A}}

) is correct because the ratio of kinetic energies is inversely proportional to the ratio of velocities due to conservation of momentum.

Solution approach

Correct Answer + Core Reason: $\mathrm{v}_{\mathrm{B}}: \mathrm{v}_{\mathrm{A}}$ . The ratio of kinetic energies is inversely proportional to the ratio of velocities due to conservation of momentum.

Step-by-Step Solution:

Step 1: Apply the law of conservation of momentum.\nSince the initial momentum is zero, the final momentum must also be zero.
$m_A v_A + m_B v_B = 0$
$m_A v_A = -m_B v_B$
$|m_A v_A| = |m_B v_B|$

Step 2: Express the kinetic energies of the two parts.
$K_A = \frac{1}{2} m_A v_A^2$
$K_B = \frac{1}{2} m_B v_B^2$

Step 3: Find the ratio of the kinetic energies.
$\frac{K_B}{K_A} = \frac{\frac{1}{2} m_B v_B^2}{\frac{1}{2} m_A v_A^2} = \frac{m_B v_B^2}{m_A v_A^2}$

Step 4: Use the conservation of momentum to relate the masses and velocities.\nSince $|m_A v_A| = |m_B v_B|$ , we have $m_A v_A = m_B v_B$ . Therefore, $m_A = \frac{{m_B v_B}}{{v_A}}$

Step 5: Substitute the expression for $m_A$ into the kinetic energy ratio.
$\frac{K_B}{K_A} = \frac{m_B v_B^2}{\frac{{m_B v_B}}{{v_A}} v_A^2} = \frac{m_B v_B^2 v_A}{m_B v_B v_A^2} = \frac{v_B}{v_A}$

Why other options are wrong:
- **Option B ( $\mathrm{m}_{\mathrm{B}}: \mathrm{m}_{\mathrm{A}}$ ): This is incorrect because it only considers the mass ratio and not the velocity ratio.
- Option C ( $\mathrm{m}_{\mathrm{B}} \mathrm{v}_{\mathrm{B}}: \mathrm{m}_{\mathrm{A}} \mathrm{v}_{\mathrm{A}}$ ): This is incorrect because the ratio is 1:1, not the ratio of kinetic energies.
- Option D ( $1: 1$ ): This is incorrect because the kinetic energies are not necessarily equal; only the magnitudes of the momenta are equal.

Key Concepts:
- Conservation of momentum
- Kinetic energy

Memory Aids:
- Remember that momentum is conserved in an isolated system.

Quick Tips:**
- Use the conservation of momentum to relate the velocities and masses.

15 Easy

15 of 34

Application +4 | -1

If a force of 260 N acts on a body the momentum required is 126 kg m/s. The period for which the force acts on the body is

View answer and explanation

Correct option: A

0.4 s

Option A (0.4 s) is correct because it is the time calculated using the impulse-momentum theorem, where the force is equal to the rate of change of momentum.

Solution approach

Correct Answer + Core Reason: 0.4 s. The time is calculated using the impulse-momentum theorem: $F = \frac{dP}{dt}$ .

Step-by-Step Solution:

Step 1: State the relationship between force and momentum: $F = \frac{dP}{dt}$ .

Step 2: Rearrange the equation to solve for the time interval $dt$ : $dt = \frac{dP}{F}$ .

Step 3: Substitute the given values: $dP = 126 \mathrm{~kg \cdot m/s}$ and $F = 260 \mathrm{~N}$ .

Step 4: Calculate the time interval: $dt = \frac{126}{260} \approx 0.485 \mathrm{~s} \approx 0.4 \mathrm{~s}$ .

Why other options are wrong:
- Option B: This answer is incorrect. It might be obtained by incorrectly applying the impulse-momentum theorem.
- Option C: This answer is incorrect. It might be obtained by incorrectly applying the impulse-momentum theorem.
- Option D: This answer is incorrect. It might be obtained by incorrectly applying the impulse-momentum theorem.

Key Concepts:
- Impulse-momentum theorem
- Force and momentum

Memory Aids:
- $F = \frac{dP}{dt}$

Quick Tips:
- Remember that the impulse is equal to the change in momentum.

16 Easy

16 of 34

Understanding +4 | -1

In case of horse pulling a cart, the force that causes the horse to move forward is the force that

View answer and explanation

Correct option: B

The ground exerts on the horse

Option B (The ground exerts on the horse) is correct because the horse pushes backward on the ground, and by Newton's third law, the ground pushes forward on the horse, propelling it forward.

Solution approach

Correct Answer + Core Reason: The ground exerts on the horse. This is due to Newton's Third Law of Motion (action-reaction pair).

Step-by-Step Solution:

Step 1: Identify the forces involved. The horse exerts a force on the ground (backward).

Step 2: Apply Newton's Third Law: For every action, there is an equal and opposite reaction.

Step 3: The ground exerts an equal and opposite force on the horse (forward). This force propels the horse forward.

Step 4: Conclusion: The force that causes the horse to move forward is the force exerted by the ground on the horse.

Why other options are wrong:
- Option A: The cart exerts on the horse: This force opposes the horse's motion and doesn't cause it to move forward.
- Option C: The horse exerts on the cart: This force causes the cart to move, not the horse itself.
- Option D: The horse exerts on the ground: This is the action force, but the reaction force is what moves the horse.

Key Concepts:
- Newton's Third Law of Motion (Action-Reaction)

Memory Aids:
- Action-Reaction pairs always act on different objects.

Quick Tips:
- Always consider the object on which the force is acting when analyzing motion.

17 Easy

17 of 34

Application +4 | -1

The average resisting force that must act on a

5 \mathrm{~kg}

mass to reduce its speed from

65

to

15 \mathrm{~ms}^{-1}

in

2 \mathrm{~s}

is

View answer and explanation

Correct option: B

125 \mathrm{~N}

Option B (125 N) is correct because the average resisting force is calculated using the impulse-momentum theorem.

Solution approach

Correct Answer + Core Reason: 125 N. The average resisting force is calculated using the impulse-momentum theorem.

Step-by-Step Solution:

Step 1: Identify given information: Mass $m = 5 \text{{ kg}}$ , initial velocity $v_i = 65 \text{{ m/s}}$ , final velocity $v_f = 15 \text{{ m/s}}$ , time interval $\Delta t = 2 \text{{ s}}$ .

Step 2: Calculate the change in momentum: $\Delta P = m(v_f - v_i) = 5(15 - 65) = 5(-50) = -250 \text{{ kg m/s}}$ .

Step 3: Apply the impulse-momentum theorem: $F_{av} \Delta t = |\Delta P|$ , where $F_{av}$ is the average force.

Step 4: Solve for the average force: $F_{av} = \frac{|\Delta P|}{\Delta t} = \frac{|-250|}{2} = 125 \text{{ N}}$ .

Step 5: Final Answer: 125 N

Why other options are wrong:
- Option A (12.5 N): This is incorrect because it likely involves a calculation error, possibly dividing the change in momentum by the mass instead of the time interval.
- Option C (1250 N): This is incorrect and may arise from a calculation error, perhaps multiplying the change in momentum by the time interval instead of dividing.
- Option D (None of these): This is incorrect as the correct answer is 125 N.

Key Concepts:
- Impulse-momentum theorem
- Average force
- Change in momentum

Memory Aids:
- $F_{av} \Delta t = \Delta P$ (Impulse-momentum theorem)

Quick Tips:
- Use the impulse-momentum theorem to relate force and change in momentum.
- Pay attention to the sign of the change in momentum.
- Ensure consistent units.

18 Easy

18 of 34

Understanding +4 | -1

Motion of the particle is non uniform when

View answer and explanation

Correct option: D

All of the above

Option D (All of the above) is correct because non-uniform motion occurs when either the direction or magnitude (speed) of the velocity changes.

Solution approach

Correct Answer + Core Reason: All of the above. Any change in velocity (direction or magnitude) results in non-uniform motion.

Step-by-Step Solution:
Step 1: Velocity is a vector quantity, having both magnitude (speed) and direction.
Step 2: Non-uniform motion implies that the velocity is changing with time.
Step 3: A change in either the magnitude (speed) or the direction of the velocity constitutes a change in velocity.
Step 4: Therefore, if the direction of velocity changes, the magnitude of velocity changes, or the speed changes, the motion is non-uniform.

Why other options are wrong:
- Option A: If the direction of velocity changes, the motion is non-uniform, but this is not the only condition.
- Option B: If the magnitude of velocity changes, the motion is non-uniform, but this is not the only condition.
- Option C: If the speed changes, the motion is non-uniform, but this is not the only condition.

Key Concepts:
- Velocity
- Speed
- Uniform and non-uniform motion

Memory Aids:
- Remember that velocity is a vector quantity.

Quick Tips:
- Understand the difference between speed and velocity.

19 Easy

19 of 34

Application +4 | -1

Two blocks of masses

M=3 \mathrm{~kg}

and

\mathrm{m}=2 \mathrm{~kg}

, are in contact on a horizontal table. A constant horizontal force

\mathrm{F}=5 \mathrm{~N}

is applied to block

\mathrm{M}

as shown. There is a constant frictional force of

2 \mathrm{~N}

between the table and the block

\mathrm{m}

but no frictional force between the table and the first block

M

, then the acceleration of the two blocks is

View answer and explanation

Correct option: B

0.6 \mathrm{~ms}^{-2}

Option B (

0.6 \mathrm{~ms}^{-2}

) is correct because the acceleration of the two blocks is determined by the net force acting on the system divided by the total mass.

Solution approach

Correct Answer + Core Reason: $0.6 \mathrm{~ms}^{-2}$ . The acceleration is calculated by considering the net force and total mass of the system.

Step-by-Step Solution:
Step 1: Identify the given values: Mass of block M, $M = 3$ kg, mass of block m, $m = 2$ kg, applied force $F = 5$ N, and frictional force on block m, $f = 2$ N.
Step 2: Calculate the net force acting on the system. The applied force is $F = 5$ N, and the frictional force opposing the motion is $f = 2$ N. Therefore, the net force is $F_{net} = F - f = 5 - 2 = 3$ N.
Step 3: Calculate the total mass of the system: $M_{total} = M + m = 3 + 2 = 5$ kg.
Step 4: Apply Newton's second law: $F_{net} = M_{total} \times a$ , where $a$ is the acceleration of the system.
Step 5: Solve for the acceleration: $a = \frac{{F_{net}}}{{M_{total}}} = \frac{3}{5} = 0.6 \text{{ m/s}}^2$ .

Why other options are wrong:
- **Option A ( $0.4 \mathrm{~ms}^{-2}$ ): This is incorrect because it may result from an incorrect calculation of the net force or total mass.
- Option C ( $0.8 \mathrm{~ms}^{-2}$ ): This is incorrect because it may result from an incorrect calculation of the net force or total mass.
- Option D ( $1 \mathrm{~ms}^{-2}$ ): This is incorrect because it may result from neglecting the frictional force.

Key Concepts:**
- Newton's second law: $F = ma$
- Net force

Memory Aids:
- Remember to consider all forces acting on the system when calculating the net force.

Quick Tips:
- Always draw a free-body diagram to identify all the forces acting on the system.

20 Easy

20 of 34

Application +4 | -1

A block is projected on a rough horizontal surface with

\mu_s=0.5

and

\mu_k=0.4

. Its initial velocity is

8 \mathrm{~m} / \mathrm{s}

. The total distance travelled by it till

t=3 \mathrm{~sec}

is:

View answer and explanation

Correct option: B

8 \mathrm{~m}

Option B (8 m) is correct because the block stops before t=3s, and the distance is calculated using kinematics with friction.

Solution approach

Correct Answer + Core Reason: 8 m. The distance traveled is calculated by first finding the acceleration due to friction and then using kinematics to determine the distance traveled until the block stops.

Step-by-Step Solution:

Step 1: Calculate the acceleration due to kinetic friction: $f_k = \mu_k mg = ma$ , so $a = \mu_k g = 0.4 \times 10 = 4 \text{ m/s}^2$

Step 2: Calculate the time it takes for the block to stop: $v = u + at$ , so $0 = 8 - 4t$ , which gives $t = 2 \text{ s}$

Step 3: Calculate the distance traveled until the block stops: $v^2 = u^2 + 2as$ , so $0 = 8^2 - 2 \times 4 \times s$ , which gives $s = \frac{64}{8} = 8 \text{ m}$

Step 4: Since the block stops at t=2s, and we are asked for the distance at t=3s, the distance remains the same after t=2s.

Why other options are wrong:
- Option A (6 m): This is incorrect because it likely involves an error in the calculation of the distance using kinematics.
- Option C (1.5 m): This is incorrect because it likely involves an error in the calculation of the distance using kinematics.
- Option D (9 m): This is incorrect because it likely involves an error in the calculation of the distance using kinematics.

Key Concepts:
- Kinetic friction
- Equations of motion

Memory Aids:
- Remember that friction opposes motion.

Quick Tips:
- Always check if the object stops before the given time.
- Use the appropriate equation of motion based on the given information.

21 Easy

21 of 34

Analyzing +4 | -1

Choose the wrong statement

View answer and explanation

Correct option: C

If the speed of a particle is constant, its acceleration must be zero

Option C is correct because constant speed does not necessarily mean zero acceleration; uniform circular motion is an example where speed is constant, but acceleration is non-zero.

Solution approach

Correct Answer + Core Reason: If the speed of a particle is constant, its acceleration must be zero. This is incorrect because uniform circular motion has constant speed but non-zero acceleration.

Step-by-Step Solution:

Step 1: Analyze the statements:

Step 2: Statement A: Zero-velocity of a particle at any instant does not necessarily mean that its acceleration is zero. (True, e.g., a ball thrown upwards at its highest point).

Step 3: Statement B: Zero acceleration of a particle at any instant does not necessarily mean that its velocity is zero. (True, e.g., a car at rest with no net force).

Step 4: Statement C: If the speed of a particle is constant, its acceleration must be zero. (False, e.g., uniform circular motion).

Step 5: In uniform circular motion, the speed is constant, but the direction of velocity changes continuously, resulting in centripetal acceleration.

Why other options are wrong:
- Option A: Statement C is wrong.
- Option B: Statement C is wrong.
- Option D: Statement C is wrong.

Key Concepts:
- Acceleration
- Velocity
- Uniform circular motion

Memory Aids:
- Constant speed does not imply zero acceleration if the direction is changing.

Quick Tips:
- Remember that acceleration is the rate of change of velocity, which includes both magnitude and direction.

22 Easy

22 of 34

Understanding +4 | -1

Which of the following statement (s) is/are incorrect?

View answer and explanation

Correct option: B

Friction always opposes the motion of two bodies.

Option B is correct because friction opposes the *relative* motion between two surfaces in contact, not necessarily the motion of the bodies themselves. Static friction can even help initiate motion (e.g., walking).

Solution approach

Correct Answer + Core Reason: Friction always opposes the motion of two bodies. Friction opposes relative motion, not necessarily the motion of the bodies.

Step-by-Step Solution:

Step 1: Understand friction: Friction is a force that opposes the relative motion or tendency of relative motion between two surfaces in contact.

Step 2: Analyze the statement: The statement "Friction always opposes the motion of two bodies" is incorrect because friction opposes the *relative* motion between the bodies. For example, when walking, static friction between your feet and the ground actually helps you move forward.

Step 3: Correct the statement: A more accurate statement would be "Friction always opposes the *relative* motion between two bodies in contact.".

Why other options are wrong:
- Option A: Static friction is self-adjusting (up to a maximum value), while kinetic friction is approximately constant. This statement is correct.
- Option C: Without friction, it would be impossible to move on a smooth surface. This statement is correct.
- Option D: Air friction does cause some mechanical energy to be lost in the form of heat. This statement is correct.

Key Concepts:
- Static friction
- Kinetic friction
- Relative motion

Memory Aids:
- Friction opposes *relative* motion.

Quick Tips:
- Always consider the relative motion between surfaces when analyzing friction.

23 Easy

23 of 34

Remembering +4 | -1

In the above ques., the height to which the lift takes the passenger is

View answer and explanation

Correct option: D

36 meters

The correct answer is D (36 meters) because the distance traveled is the area under the velocity-time graph, which calculates to 36 meters.

Solution approach

Correct Answer + Core Reason: 36 meters. The height is calculated by finding the area under the velocity-time graph.

Step-by-Step Solution:

Step 1: Recognize that the distance traveled is the area under the velocity-time graph.

Step 2: Divide the graph into three sections: a triangle, a rectangle, and another triangle.

Step 3: Calculate the area of the first triangle: $\frac{{1}}{{2}} \times 2 \times 3.6 = 3.6$ meters.

Step 4: Calculate the area of the rectangle: $8 \times 3.6 = 28.8$ meters.

Step 5: Calculate the area of the second triangle: $\frac{{1}}{{2}} \times 2 \times 3.6 = 3.6$ meters.

Step 6: Add the three areas: $3.6 + 28.8 + 3.6 = 36$ meters.

Step 7: Conclusion: The height to which the lift takes the passenger is 36 meters.

Why other options are wrong:
- Option A: 3.6 meters is the height reached during the acceleration/deceleration phases only.
- Option B: 8 meters is not related to the area under the curve.
- Option C: 1.8 meters is not related to the area under the curve.
- Option D: 36 meters is the correct answer, representing the total distance traveled.

Key Concepts:
- Velocity-time graph
- Area under the curve
- Distance traveled

Memory Aids:
- Area under v-t graph = displacement

Quick Tips:
- Always remember to calculate the area under the curve for distance in v-t graphs.

24 Easy

24 of 34

Understanding +4 | -1

A particle of mass

m

is moving with a uniform velocity

v_1

. It is given an impulse such that its velocity becomes

v_2

. The impulse is equal to

View answer and explanation

Correct option: D

{m}\left({v}_2-{v}_1\right)

Option D

{m}\left({v}_2-{v}_1\right)

is correct because impulse is defined as the change in momentum, which is mass times the change in velocity.

Solution approach

Correct Answer + Core Reason: ${m}\left({v}_2-{v}_1\right)$ . Impulse is equal to the change in momentum.

Step-by-Step Solution:

Step 1: Define impulse. Impulse (J) is the change in momentum of an object.

Step 2: Write the formula for impulse. Impulse, $J = \Delta p = p_f - p_i$ , where $p_f$ is the final momentum and $p_i$ is the initial momentum.

Step 3: Express momentum in terms of mass and velocity. Momentum, $p = mv$ , where m is mass and v is velocity.

Step 4: Substitute the expressions for initial and final momentum into the impulse formula. $J = mv_2 - mv_1$

Step 5: Factor out the mass. $J = m(v_2 - v_1)$

Why other options are wrong:
- Option A: ${m}\left[\left|{v}_2\right|-\left|{v}_1\right|\right]$ : This is incorrect because it only considers the magnitudes of the velocities and not the direction. Impulse is a vector quantity, so direction matters.
- Option B: $\frac{1}{2} {~m}\left({v}_2^2-{v}_1^2\right)$ : This represents the change in kinetic energy, not the impulse. Kinetic energy is a scalar quantity, while impulse is a vector quantity related to momentum.
- Option C: ${m}\left({v}_1+{v}_2\right)$ : This is incorrect because it represents the mass times the sum of the initial and final velocities, which is not equal to the impulse (change in momentum).

Key Concepts:
- Impulse
- Momentum
- Change in Momentum

Memory Aids:
- Impulse = Change in Momentum

Quick Tips:
- Remember that impulse and momentum are vector quantities.
- Pay attention to the direction of the velocities when calculating impulse.

25 Easy

25 of 34

Understanding +4 | -1

When a ball is whirled in a circle and the string supporting the ball is released, the ball flies off tangentially. This is due to

View answer and explanation

Correct option: B

inertia for linear motion

Option B (inertia for linear motion) is correct because the ball continues to move in a straight line due to its inertia when the string is released.

Solution approach

Correct Answer + Core Reason: inertia for linear motion. When the string is released, the ball flies off tangentially due to its inertia to maintain its linear motion.

Step-by-Step Solution:
Step 1: The ball is moving in a circle due to the centripetal force provided by the string.
Step 2: When the string is released, the centripetal force vanishes.
Step 3: According to Newton's first law (inertia), the ball will continue to move in the direction it was moving at the instant the string was released.
Step 4: This direction is tangential to the circle.
Step 5: Therefore, the ball flies off tangentially due to inertia.

Why other options are wrong:
- Option A: Centrifugal force is a fictitious force and not the reason for the ball's motion.
- Option C: Centripetal force is the force that keeps the ball moving in a circle, but it disappears when the string is released.
- Option D: The cause is well-known: inertia.

Key Concepts:
- Inertia
- Newton's First Law of Motion
- Centripetal Force

Memory Aids:
- Inertia: Objects resist changes in their state of motion.

Quick Tips:
- Remember that inertia causes objects to maintain their current state of motion.

26 Easy

26 of 34

Application +4 | -1

A marble block of mass 3 kg lying on ice when given a velocity of 6 m/s it stopped by friction in 12 s. Then the coefficient of friction is

\left( {g = 10\,\,m/{s^2}} \right)

View answer and explanation

Correct option: A

0.05

Option A (0.05) is correct because it's the coefficient of friction, calculated using the kinematic equation and the relationship between friction and acceleration.

Solution approach

Correct Answer + Core Reason: 0.05. The coefficient of friction is calculated using kinematics and the relationship between friction and acceleration.

Step-by-Step Solution:

Step 1: Initial velocity (u) = 6 m/s

Step 2: Final velocity (v) = 0 m/s

Step 3: Time (t) = 12 s

Step 4: Acceleration (a) = $\frac{{v - u}}{t} = \frac{{0 - 6}}{{12}} = -0.5 m/s^2$

Step 5: Friction force (f) = $ma = 3 \times (-0.5) = -1.5 N$

Step 6: Friction force (f) = $\mu N = \mu mg$

Step 7: $\mu mg = 1.5$

Step 8: $\mu = \frac{{1.5}}{{mg}} = \frac{{1.5}}{{3 \times 10}} = \frac{{1.5}}{{30}} = 0.05$

Why other options are wrong:
- Option B: Incorrect calculation.
- Option C: Incorrect calculation.
- Option D: Incorrect calculation.

Key Concepts:
- Kinematics
- Friction
- Newton's second law

Memory Aids:
- Remember $v = u + at$ and $f = \mu N$

Quick Tips:
- Pay attention to the sign of acceleration.

27 Easy

27 of 34

Application +4 | -1

A brick of mass 3 kg just begins to side down on inclined plane at an angle of

60^\circ

with the horizontal. The force of friction will be

View answer and explanation

Correct option: A

29.4\,\sin 60^\circ \,

Option A (

29.4\\,\sin 60^\circ \,

) is correct because the force of friction equals the component of weight along the inclined plane when the brick just begins to slide.

Solution approach

Correct Answer + Core Reason: $29.4\\,\sin 60^\circ \,$ . The friction force is equal to the component of weight along the inclined plane.

Step-by-Step Solution:

Step 1: Identify the given information: Mass $m = 3\,\,kg$ , angle of inclination $\theta = 60^\circ$ .

Step 2: Recall the formula for the component of weight along the inclined plane: $F_\text{parallel} = mg\sin\theta$

Step 3: At the point when the brick just begins to slide, the force of friction is equal to the component of weight along the inclined plane: $f = mg\sin\theta$

Step 4: Substitute the given values: $f = 3 \times 9.8 \times \sin 60^\circ$

Step 5: Calculate the force of friction: $f = 29.4\sin 60^\circ \,N$

Why other options are wrong:
- **Option B ( $28.4\\,\sin 60^\circ$ ): This is incorrect. It likely arises from using an incorrect value for the acceleration due to gravity or a calculation error.
- Option C ( $29.4\\,\cos 60^\circ$ ): This is incorrect. It uses the cosine of the angle instead of the sine, which is the component of weight perpendicular to the plane, not along it.
- Option D ( $28.4\\,\cos 60^\circ$ ): This is incorrect. It uses both an incorrect value (28.4 instead of 29.4) and the cosine of the angle instead of the sine.

Key Concepts:
- Components of weight on an inclined plane
- Static friction

Memory Aids:**
- Remember that the component of weight along the inclined plane is $mg\sin\theta$ .

Quick Tips:
- Always draw a free-body diagram to visualize the forces acting on the object.
- Ensure you are using the correct trigonometric function (sine or cosine) for the component you are calculating.

28 Easy

28 of 34

Understanding +4 | -1

Statement-I: If net force on a rigid body is zero, it is either at rest or moving with a constant linear velocity.
Statement-II: Constant velocity means linear acceleration is zero

View answer and explanation

Correct option: A

Statement-I is true and statement-II is true

Option A (Statement-I is true and statement-II is true) is correct because a zero net force implies either rest or constant velocity (Newton's First Law), and constant velocity inherently means zero acceleration.

Solution approach

Correct Answer + Core Reason: Statement-I is true and statement-II is true. Zero net force implies constant velocity (including zero), and constant velocity implies zero acceleration.

Step-by-Step Solution:

Step 1: Analyze Statement-I: If the net force on a rigid body is zero, then according to Newton's First Law (Law of Inertia), the body will either remain at rest or continue to move with a constant linear velocity. This statement is true.

Step 2: Analyze Statement-II: Constant velocity means that the rate of change of velocity with respect to time is zero. Since acceleration is defined as the rate of change of velocity, constant velocity implies zero acceleration. This statement is also true.

Step 3: Consider the possibility of rotational motion. While a net force of zero implies no linear acceleration, it doesn't preclude rotational motion if there's a net torque. However, the statement only addresses linear velocity and force, so it remains true within that context.

Step 4: Conclude that both statements are true.

Why other options are wrong:
- Option B (Statement-I is true and statement-II is false): Statement-II is true; constant velocity directly implies zero acceleration.
- Option C (Statement-I is false and statement-II is true): Statement-I is true; zero net force implies constant velocity (including rest).
- Option D (Statement-I is false and statement-II is false): Both statements are true.

Key Concepts:
- Newton's First Law of Motion (Law of Inertia)
- Definition of acceleration
- Net force and motion

Memory Aids:
- Newton's First Law: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net force.
- Acceleration is the rate of change of velocity.

Quick Tips:
- Remember that zero net force implies constant velocity (which can be zero).
- Constant velocity always means zero acceleration.

29 Easy

29 of 34

Analyzing +4 | -1

Statement I: A car is moving in a horizontal circular plane with varying speed, then the frictional force is neither pointing towards the radial direction nor along the tangential direction.
Statement II: Components of the frictional force are providing the necessary tangential and centripetal acceleration, in the above situation.

View answer and explanation

Correct option: A

Statement I is true, Statement II is true; Statement II is the correct explanation for Statement I

Option A is correct because the frictional force provides both the tangential and centripetal acceleration, resulting in a net force that is neither purely radial nor tangential.

Solution approach

Correct Answer + Core Reason: Statement I is true, Statement II is true; Statement II is the correct explanation for Statement I. The frictional force has both tangential and radial components, providing the necessary accelerations.

Step-by-Step Solution:
Step 1: Analyze Statement I. If the car is moving with varying speed in a circular path, it has both tangential and centripetal acceleration. The frictional force provides these accelerations. Since both accelerations are non-zero, the net force (and hence the frictional force) is neither purely radial nor purely tangential.
Step 2: Analyze Statement II. The tangential component of the frictional force provides the tangential acceleration, which changes the speed of the car. The radial component of the frictional force provides the centripetal acceleration, which keeps the car moving in a circle.
Step 3: Combine the analysis. Statement I is true because the frictional force has both tangential and radial components. Statement II is true and correctly explains why Statement I is true.

Why other options are wrong:
- Option B: Incorrect because Statement II is the correct explanation for Statement I.
- Option C: Incorrect because Statement II is true.
- Option D: Incorrect because Statement I is true.

Key Concepts:
- Circular motion
- Tangential and centripetal acceleration
- Frictional force

Memory Aids:
- Remember that tangential acceleration changes speed, and centripetal acceleration changes direction.

Quick Tips:
- Draw a free-body diagram to visualize the forces acting on the car.

30 Easy

30 of 34

Understanding +4 | -1

If the coefficient of friction is 1, the angle of friction is

View answer and explanation

Correct option: B

45^\circ

Option B (

45^\circ

) is correct because the angle of friction is the arctangent of the coefficient of friction, and when the coefficient of friction is 1, the angle is 45 degrees.

Solution approach

Correct Answer + Core Reason: $45^\circ$ . The angle of friction is the arctangent of the coefficient of friction.

Step-by-Step Solution:

Step 1: Recall the relationship between the angle of friction ( $\theta$ ) and the coefficient of friction ( $\mu$ ): $\tan \theta = \mu$ .

Step 2: Given $\mu = 1$ , we have $\tan \theta = 1$ .

Step 3: Solve for $\theta$ : $\theta = \arctan(1) = 45^\circ$ .

Why other options are wrong:
- Option A: $\tan 37^\circ$ is not equal to 1.
- Option C: $\tan 52^\circ$ is not equal to 1.
- Option D: $\tan 60^\circ$ is not equal to 1.

Key Concepts:
- Angle of friction
- Coefficient of friction

Memory Aids:
- Tangent of the angle of friction equals the coefficient of friction.

Quick Tips:
- Remember the trigonometric values for common angles.

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