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JEE • PHYSICS • MOTION IN PLANE

Motion in plane practice · Easy

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 40 questions

1 Easy

1 of 40

Application +4 | -1

The angle between two vectors given by

6 \hat{i}+6 \hat{j}-3 \hat{k}

and

7 \hat{i}+4 \hat{j}+4 \hat{k}

is :-

View answer and explanation

Correct option: D

\sin ^{-1}\left(\frac{\sqrt{5}}{3}\right)

Option D (

\sin ^{-1}(\frac{\sqrt{5}}{3})

) is correct because the angle between the vectors is found using the dot product formula, and then converting cosine to sine.

2 Easy

2 of 40

Understanding +4 | -1

Unit vector

I. has dimensions and a unit.

II. when multiplied by a scalar quantity, it results a scalar.

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

View answer and explanation

Correct option: C

Both I and II

Option C (Both I and II) is correct because a unit vector is dimensionless and when multiplied by a scalar, it results in a vector.

3 Easy

3 of 40

Understanding +4 | -1

Which of the following not a vector quantity?

View answer and explanation

Correct option: D

Potential energy

Option D (Potential energy) is correct because potential energy is a scalar quantity, while weight, nuclear spin, and momentum are vector quantities.

4 Easy

4 of 40

Application +4 | -1

\mathrm{~A}

ball is projected from ground with a speed of

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

at an angle of

45^{\circ}

with horizontal. There is a wall of

25 \mathrm{~m}

height at a distance of

10 \mathrm{~m}

from the projection point. The ball will hit the wall at a height of

View answer and explanation

Correct option: B

7.5 \mathrm{~m}

Option B (

7.5 \mathrm{~m}

) is correct because it is the height at which the ball hits the wall, calculated using projectile motion equations.

5 Easy

5 of 40

Understanding +4 | -1

The component of a vector along any other direction is

View answer and explanation

Correct option: A

always less than its magnitude

Option A (always less than its magnitude) is correct because the component of a vector along any direction is the magnitude of the vector multiplied by the cosine of the angle between them, which is always less than or equal to 1.

6 Easy

6 of 40

Application +4 | -1

The greatest height to which a man can throw a stone is

h

. The greatest distance to which he can throw it will be

View answer and explanation

Correct option: C

2 h

Option C (

2 h

) is correct because the maximum horizontal range of a projectile is twice the maximum height when the initial velocity is the same.

7 Easy

7 of 40

Analyzing +4 | -1

Two particles are projected from the same point with the same speed, at different angles

\theta_1

and

\theta_2

to the horizontal. They have the same horizontal range. Their times of flight are

t_1

and

t_2

respectively incorrect statement is.

View answer and explanation

Correct option: C

\frac{t_1}{t_2}=\tan \theta_2

Option C (

\frac{t_1}{t_2}=\tan \theta_2

) is correct because the correct relationship is

\frac{t_1}{t_2} = \frac{\sin \theta_1}{\sin \theta_2}

, and since

\theta_2 = 90 - \theta_1

\frac{t_1}{t_2} = \tan \theta_1

8 Easy

8 of 40

Application +4 | -1

Vector

\vec{A}

makes equal angles with

x, y

and

z

-axis. Value of its components (in terms of magnitude of

\vec{A}

) will be

View answer and explanation

Correct option: A

\frac{A}{\sqrt{3}}

Option A (

\frac{A}{\sqrt{3}}

) is correct because when a vector makes equal angles with all axes, its components are equal and related to its magnitude by

\frac{A}{\sqrt{3}}

9 Easy

9 of 40

Analyzing +4 | -1

I.Inprojectilemotion,theanglebetwee instantaneousvelocityvectorandacceleration vector can be anything between 0 to

\pi

(excluding the limiting case.)

II. In projectile motion, acceleration vector is always pointing vertically downwards. (Neglect air friction).

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

View answer and explanation

Correct option: C

Both I and II

Option C (Both I and II) is correct. In projectile motion, the angle between instantaneous velocity and acceleration varies from 0 to

\pi

, and the acceleration vector always points downwards (neglecting air friction).

10 Easy

10 of 40

Remembering +4 | -1

Which of the following is vector quantity?

View answer and explanation

Correct option: D

Impulse

Option D (Impulse) is correct because impulse is defined as the change in momentum, which is a vector quantity.

11 Easy

11 of 40

Application +4 | -1

\vec{A}=4 \hat{i}+3 \hat{j}

and

\vec{B}=4 \hat{i}+2 \hat{j}

. Find a vector parallel to

\vec{A}

but has magnitude five times that of

\vec{B}

View answer and explanation

Correct option: B

\sqrt{20}(4 \hat{i}+3 \hat{j})

Option B (

\sqrt{20}(4 \hat{i}+3 \hat{j})

) is correct because it finds a vector parallel to

\vec{A}

with a magnitude five times that of

\vec{B}

12 Easy

12 of 40

Understanding +4 | -1

If air resistance is not considered in projectiles, the horizontal motion takes place with

View answer and explanation

Correct option: A

constant velocity.

Option A (constant velocity) is correct because, without air resistance, there is no horizontal force acting on the projectile, so its horizontal velocity remains constant.

13 Easy

13 of 40

Understanding +4 | -1

When a projectile is fired at an angle

\theta

wrt. horizontal with velocity

u

, then its vertical component

View answer and explanation

Correct option: C

goes on decreasing with height.

The correct answer is C (goes on decreasing with height) because the vertical component of velocity decreases due to gravity.

14 Easy

14 of 40

Application +4 | -1

A body projected with velocity

u

at projection angle

\theta

has horizontal range

R

. For the same velocity and projection angle, its range on the moon surface will be

\left(g_{\text {moon }}=g_{\text {earth }} / 6\right)

View answer and explanation

Correct option: D

6 R

Option D (6 R) is correct because the range is inversely proportional to the acceleration due to gravity, and the moon's gravity is 1/6th of Earth's.

15 Easy

15 of 40

Understanding +4 | -1

As a rocket is accelerating vertically upwards at

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

near the earth's surface, it releases a projectile with zero speed relative to rocket. Immediately after release, the acceleration (in

\mathrm{ms}^{-2}

) of the projectile is [take,

g=9.8 \mathrm{~ms}^{-2}

]

View answer and explanation

Correct option: C

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

, down

Option C is correct because immediately after release, the projectile is only under the influence of gravity, resulting in a downward acceleration of 9.8 m/s².

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16 Easy

16 of 40

Understanding +4 | -1

If a vector

\vec P

make angles

\alpha ,\,\beta ,

and

\gamma

respectively with the

X,\,\,Y

and

Z

axes. Then

{\sin ^2}\alpha \,\, + \,\,{\sin ^2}\beta \,\, + \,\,{\sin ^2}\gamma \,\, =

View answer and explanation

Correct option: C

Option C (2) is correct because the sum of the squares of the sines of the angles is equal to 2.

17 Easy

17 of 40

Understanding +4 | -1

Four bodies

P,\,Q,\,R

and

S

are projected with equal velocities having angles of projection

15^\circ ,\,30^\circ ,\,45^\circ

and

60^\circ

with the horizontal respectively. The body having shortest range is

View answer and explanation

Correct option: A

P

Option A is correct. The range of a projectile is shortest when the angle of projection is farthest from 45 degrees, and 15 degrees is the farthest from 45 degrees among the given options.

18 Easy

18 of 40

Application +4 | -1

The equation of projectile is

y = 12x - \frac{{{x^2}}}{6}

. The horizontal range is

View answer and explanation

Correct option: B

72 m

Option B (72 m) is correct because it is the horizontal range calculated from the given projectile equation.

19 Easy

19 of 40

Application +4 | -1

A grasshopper can jump a maximum distance of

1.6 \mathrm{~m}

. How far can it go in

10 \mathrm{~s}

View answer and explanation

Correct option: C

20 \sqrt{2} \mathrm{~m}

Option C (

20 \sqrt{2} \mathrm{~m}

) is correct because it calculates the total distance covered by the grasshopper in 10 seconds based on its maximum jump distance.

20 Easy

20 of 40

Application +4 | -1

Train

A

is moving along two parallel rail tracks towards north with speed

72 \mathrm{~km} / \mathrm{h}

and train

B

is moving towards south with speed

108 \mathrm{~km} / \mathrm{h}

. Velocity of train

B

with respect to

A

and velocity of ground with respect to

B

are (in

\mathrm{ms}^{-1}

)

View answer and explanation

Correct option: C

-50 and 30

Option C ( -50 and 30) is correct because it correctly calculates the relative velocities using vector subtraction.

21 Easy

21 of 40

Remembering +4 | -1

Identify the vector quantity among the following

View answer and explanation

Correct option: C

Angular momentum

Option C (Angular momentum) is correct because angular momentum has both magnitude and direction, making it a vector quantity.

22 Easy

22 of 40

Understanding +4 | -1

Statement-I: Angle between

\hat{i}+\hat{j}

and

\hat{i}

45^{\circ}

.
Statement-II:

\hat{i}+\hat{j}

is equally inclined to both

\hat{i}

and

\hat{j}

and the angle between

\hat{i}

and

\hat{j}

90^{\circ}

View answer and explanation

Correct option: A

Statement-I is true and statement-II is true

Option A is correct because the angle between

\hat{i}+\hat{j}

and

\hat{i}

is indeed

45^{\circ}

, and

\hat{i}+\hat{j}

is equally inclined to both

\hat{i}

and

\hat{j}

23 Easy

23 of 40

Understanding +4 | -1

Assertion At highest point of a projectile, dot product of velocity and acceleration is zero.

Reason At highest point, velocity and acceleration are mutually perpendicular.

View answer and explanation

Correct option: A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Option A (If both Assertion and Reason are correct and Reason is the correct explanation of Assertion) is correct because at the highest point, the velocity is horizontal and the acceleration due to gravity is vertical, making them perpendicular and their dot product zero.

24 Easy

24 of 40

Application +4 | -1

\mathbf{A}

and

\mathbf{B}

are two vectors given by

\mathbf{A}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}

and

\mathbf{B}=2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}

. The magnitude of the component of

\mathbf{A}

along

\mathbf{B}

View answer and explanation

Correct option: C

\frac{8}{\sqrt{5}}

Option C (

\frac{8}{\sqrt{5}}

) is correct because it is calculated by finding the dot product of the two vectors and dividing by the magnitude of vector B.

25 Easy

25 of 40

Application +4 | -1

When the angle of elevation of a gun are

60^\circ \,

and

30^\circ \,

respectively. The height it shoots are

{h_1}

and

{h_2}

respectively. Find the ratio

\,\frac{{{h_1}}}{{{h_2}}}

View answer and explanation

Correct option: C

0.125694444

Option C (03:01) is correct because the ratio of heights is 3:1 when the angles of elevation are 60° and 30° respectively.

26 Easy

26 of 40

Application +4 | -1

Projectiles

A

and

B

are thrown at angles of

45^{\circ}

and

60^{\circ}

with vertical respectively from top of a

400 \mathrm{~m}

high tower. If their ranges and times of flight are same, the ratio of their speeds of projection

v_A: v_B

is:

\text{[Take }g=10 \mathrm{~m} / \mathrm{s}^2]

View answer and explanation

Correct option: B

1: \sqrt{2}

Option B (

1: \sqrt{2}

) is correct because for the same time of flight, the vertical components of the initial velocities must be equal, leading to the given ratio.

27 Easy

27 of 40

Understanding +4 | -1

A scalar quantity is one that

View answer and explanation

Correct option: D

has the same value for observers with different orientations of axes.

The correct answer is D (has the same value for observers with different orientations of axes) because a scalar quantity is defined by its magnitude and is independent of coordinate system orientation.

28 Easy

28 of 40

Analyzing +4 | -1

Assertion(A): When

\theta=45^{\circ}

135^{\circ}

, the value of

R

remains the same, only the sign changes.

Reason(R):

R=\frac{u^2 \sin 2 \theta}{g}

View answer and explanation

Correct option: A

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Option A (Both Assertion and Reason are correct and Reason is the correct explanation of Assertion) is correct because the range is the same for complementary angles, and the reason correctly states the formula for the range.

29 Easy

29 of 40

Application +4 | -1

If a unit vector is represent by

0.5 \hat{\mathbf{i}}+0.8 \hat{\mathbf{j}}+c \hat{\mathbf{k}}

, then the value of

c

View answer and explanation

Correct option: B

\sqrt{0.11}

Option B (

\sqrt{0.11}

) is correct because the magnitude of a unit vector must be 1, and this value of c satisfies that condition.

30 Easy

30 of 40

Analyzing +4 | -1

Assertion If a particle is projected vertically upwards with velocity

u

, the maximum height attained by the particle is

h_1

. The same particle is projected at angle

30^{\circ}

from horizontal with the same speed

u

. Now the maximum height is

h_2

. Thus,

h_1=4 h_2

.

Reason In first case,

v=0

at highest point and in second case,

v \neq 0

at highest point.

View answer and explanation

Correct option: B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

Option B (If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion) is correct because both the assertion about the heights and the reason about velocities at the highest point are true, but the reason doesn't explain the assertion.

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Key Takeaways

✓ This set contains 40 single-correct-answer MCQs on MOTION IN PLANE.
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