Laws of motion practice · Mixed difficulty

Option D (If both Assertion & Reason are false) is correct because frictional force is non-conservative, and the work done by it in a round trip is not zero.

Option A (${F}=\frac{{dp}}{{dt}}$) is correct because it is the correct mathematical representation of Newton's second law, stating that force equals the rate of change of momentum.

Option C ($5 \times {10^{ - 1}}N$) is correct because the force exerted on the plate is equal to the rate of change of momentum of the water.

Option C (480) is correct because the average force is calculated using the change in momentum of the bullets.

Option D is correct because action and reaction forces always act on different bodies, and none of the given pairs satisfy this condition.

Option B ($\frac{7}{10} \frac{v^2}{g}$) is correct because the total kinetic energy (translational + rotational) is converted into potential energy.

Option D (If both assertion and reason are false) is correct because kinetic friction is not self-adjusting and does depend on the normal force, which is related to the mass.

Option B (180) is correct because it is the average force calculated using the rate of change of momentum of the bullets hitting the plate.

Option C (There is an acceleration because there is a momentum change) is correct because acceleration is related to the change in velocity, which is directly related to the change in momentum.

Option B (2 m/s) is correct because the speed at A is calculated using the conservation of energy principle, equating potential energy at height h to kinetic energy at point A.

Option A is correct because if the net external force is zero, the linear momentum of the system remains constant due to conservation of momentum.

Option A (Not changed) is correct because the coefficient of friction is a property of the surfaces in contact and is independent of the normal force.

The correct answer is C (Both 1 & 2) because net force is zero when acceleration is zero, which is true for an object moving with uniform velocity and an object at rest.

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.

Option A (Assertion is correct, reason is correct; reason is a correct explanation for assertion) is correct because static friction is generally greater than kinetic friction, and this is because the coefficient of static friction is higher than the coefficient of kinetic friction.

Option D (As the force applied is internal to the system) is correct because pulling on one's hair involves internal forces within the student's body, which cannot change the momentum of the entire system (student).

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.

Option D (Kinetic friction is self adjusting) is the incorrect statement because kinetic friction has a fixed value determined by the coefficient of kinetic friction and the normal force.

Option A (T) is correct because the net force on the particle directed towards the center is provided by the tension in the string.

Option B ($v \sqrt{5}$) is correct because it is the speed of the second sphere calculated using conservation of momentum in two dimensions.

Option C (0.75) is correct because using the formula $\mu = \tan \theta (1 - \frac{{1}}{{{n^2}}})$ with $\theta = 45^\circ$ and n=2, we get $\mu = 0.75$.

Option A (Statement I is true, Statement II is true, Statement II is the correct explanation for Statement I) is correct because the push of the rear axle on the wheels is the accelerating force, and this push is due to the rotation of the axle at a greater frequency.

Option B (20 N) is correct because the frictional force equals the weight of the body, preventing it from falling.

Option A ($120 \mathrm{~ms}^{-1}$) is correct because it is the velocity of the remaining part calculated using the conservation of momentum.

Option A ($0^{\circ}$) is correct because impulse and change in momentum are in the same direction according to the impulse-momentum theorem.

Option A is correct because pushing a lawn roller increases the effective weight, leading to higher friction, making it harder to pull.

Option D ($8:1$) is correct because the ratio of velocities is inversely proportional to the ratio of masses, which is related to the cube of the radii ratio.

Option B (Statement-I is true and statement-II is false) is correct because the coefficient of friction can be greater than unity, but the statement about the ratio of friction and normal reaction is misleading.

Option D (Keep it moving with uniform velocity) is correct because, according to Newton's first law, an object in motion stays in motion with the same speed and direction unless acted upon by a force.

Option C (both 1 & 2) is correct because a smaller time interval requires a larger force to achieve the same change in momentum, and vice versa, as dictated by the impulse-momentum theorem.