Laws of motion practice · Mixed difficulty

Option C is correct. Statement I is true because the rifle's kinetic energy is less than the bullet's due to the rifle's larger mass. Statement II is false because momentum is conserved in the rifle-bullet system.

Option D ($5\sqrt 2 \;\mathrm{m}{\mathrm{s}^{ - 1}}$) is correct because the maximum speed is proportional to the square root of the coefficient of friction.

Option D (They move with same speed in opposite directions) is correct because due to conservation of momentum, the two equal parts must move with equal speeds in opposite directions to maintain zero total momentum.

Option D is correct because rolling friction is generally less than kinetic friction, which is less than static friction.

Option B (If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion) is correct because mass is an intrinsic property while weight is due to gravitational interaction, and weight is proportional to mass, but the latter doesn't explain the former.

Option C (The momentum of the particle constant) is correct because, according to Newton's first law, if the momentum of a particle is constant, the net force acting on it is zero.

The correct answer is C because the assertion is true (a body can be at rest with multiple forces), but the reason is false (forces need to have a zero resultant, not just be concurrent).

Option C is correct because both the man and the bag experience the same acceleration due to gravity, resulting in the same final velocity after falling from the same height.

The correct answer is B because both statements are true, but the reason doesn't explain the assertion; Statement I is about friction, and Statement II is about the absence of friction.

Option A (72) is correct because the tension in the string is calculated using T = m(g + a).

Option D (0) is correct because when the rope breaks, the lift is in freefall, and the tension exerted by the surface of the lift is zero.

Option A is correct because both statements are true and statement II correctly explains statement I based on the relationship between force and time.

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.

The correct answer is D (Statement- 1 is false, Statement-2 is true) because the scale reading will decrease as the man squats down, and the man does push down on the scale.

Option A (3 sec) is correct because it correctly calculates the time at which the car will skid based on the given parameters.

Option C is correct because the Assertion is true (apparent weight is less when moving downwards), but the Reason is false (the force is due to acceleration, not the lift itself).

Option B (Assertion is correct, reason is correct; reason is not a correct explanation for assertion) is correct because both statements are true, but the conservation of momentum doesn't directly explain why equal force over equal time causes equal momentum change.

Option A ($\frac{{7 p^2}}{{24 m}}$) is correct because it is derived from the conservation of momentum and the calculation of kinetic energy of the fragments.

Option D (zero) is correct because when the raindrop falls with constant speed, the net force acting on it is zero due to balanced forces.

Option D is correct because inertia is the property of a body that resists any change in its state of rest or uniform motion.

Option B is correct because the passengers fall forward due to inertia, as described by Newton's first law.

Option A (3) is correct because the maximum number of bullets fired per second is determined by the maximum force the man can exert divided by the momentum change per bullet.

Option B (100 N/m) is correct because the spring constant is calculated by equating the weight of the water to the spring force.

Option C is correct because the assertion is true (tension acts away from the body), but the reason is false (friction opposes motion, not necessarily related to tension).

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.

Option B (The average elastic force acting on the balls is $\frac{2 m(u+v)}{\Delta t}$) is correct because it is derived from the change in momentum of the ball during the elastic collision with the massive wall.

Option C ($60 {~N}$) is correct because, according to Newton's third law, the force exerted by the 40 kg man on the 60 kg man is equal in magnitude and opposite in direction to the force exerted by the 60 kg man on the 40 kg man.

Option B (0.4) is correct because the coefficient of friction is calculated using the relationship between acceleration, gravity, and the coefficient of friction: $a = -\mu g$.

Option B is correct because constant momentum implies constant velocity for a body with constant mass.

Option B (I, II and III) is correct because inertia of rest, motion, and direction are the three fundamental types of inertia.