Laws of motion practice · Medium

Option A ($6 \,\mathrm{Ns}$) is correct because the impulse is equal to the change in momentum of the bullet.

Option B (9.8 m) is correct because the distance is calculated using the kinematic equation and the deceleration due to friction.

Option B (160000 N) is correct because the force exerted on the rocket is calculated by multiplying the rate of fuel burn by the ejection velocity.

Option B (Mass, motion and force) is correct because these are the fundamental concepts used to describe and analyze the behavior of objects in Newtonian mechanics.

Option C (Its linear momentum will be more than double) is correct because as velocity approaches the speed of light, the relativistic mass increases, causing a greater increase in momentum than just doubling the velocity.

Option D (I does not imply II but II implies I) is correct because if the kinetic energy of a system of particles is zero, all particles must be at rest, implying zero linear momentum. However, zero linear momentum does not necessarily imply zero kinetic energy, as particles could have momenta that sum to zero while still moving.

Option A (3) is correct because it's the maximum number of bullets that can be fired per second based on the force the man can exert.

Option B (1.732) is correct because the coefficient of static friction is equal to the tangent of the angle of repose, which is $\tan 60^\circ = 1.732$.

Option C (Rolling friction is greater than sliding friction) is not true because rolling friction is generally much less than sliding friction.

Option B ($2.35$) is correct because it is calculated using the formula $a = g[\sin \theta - \mu _k\cos \theta ]$ with the given angle and coefficient of friction.

Option B ($B$ will be accelerated, but $A$ will be retarded) is correct because the packets transferred from A to B carry momentum, causing B to accelerate and A to decelerate.

Option B is correct because both the assertion and the reason are true, but the reason doesn't correctly explain why every part of the body experiences an inward force on a roundabout. The inward force is due to centripetal force, not an outward push.

Option B (33.30%) is correct because it represents the maximum percentage of the chain's length that can hang over the edge, determined by the coefficient of friction.

Option B (300 m) is correct because the distance is calculated using the formula distance = velocity x time, where velocity is derived from linear momentum.

Option A (17.6 kg m s⁻¹) is correct because the momentum is calculated by multiplying mass and velocity, and the result is rounded to the correct number of significant digits.

The correct answer is C (Motion with constant momentum along a straight line) because, according to Newton's first law, an object in motion with constant momentum requires no net force to maintain that motion.

Option B ($\theta=\tan ^{-1}(\mu)$) is correct because it represents the condition for equilibrium on an inclined plane, where the angle of inclination equals the inverse tangent of the coefficient of friction.

Option B is correct because Newton's Second Law, F=ma, directly quantifies the force acting on an object.

Option A is correct because a body can be at rest under multiple forces if their vector sum is zero, which is the condition for equilibrium.

Option C ($30^\circ$) is correct because it satisfies the given condition relating the forces required to move the body up and prevent it from sliding down the inclined plane, considering the coefficient of friction.

Option B (10 N) is correct because the average force exerted by the surface on the ball is calculated using the change in momentum and the time of contact.

Option A is correct because mountain roads are built with a gradual slope to reduce the required force and prevent slipping, and the reason correctly explains why steeper slopes increase the risk of slipping.

Option A ($\frac{2}{5}$) is correct because the final velocity of the boat is calculated using the conservation of linear momentum.

Option B is correct. Statement-I is true because when the lift is at rest, the resultant force on the person is equal to their weight. Statement-II is false because when the lift moves with uniform velocity, the apparent weight of the man is equal to his actual weight, not zero.

Option A is correct because if two particles undergo the same displacement, the work done by the Newton's third law pair forces on them is of opposite sign and equal magnitude, potentially summing to zero.

Option A is correct because static friction is a self-adjusting force that opposes the applied force up to a certain limit.

Option C is correct because the frictional force exerted by the surface on a person walking is in the direction of motion, and the force exerted by the road causes the motion.

Option B (0.75) is correct because the coefficient of friction is calculated by dividing the retarding acceleration by the acceleration due to gravity: $\mu = \frac{a}{g}$.

Option A ([A] and [R] are true and [R] is correct explanation of [{A}]) is correct because both the assertion and reason are true, and the reason correctly explains why the boy feels more pain on a hard floor.

Option A is correct because the resultant of the four forces of magnitude F₁ cancels out, leaving only the force F₂ - F₁.