Formula: \(F = v \frac{dm}{dt} = 20 \times 2 = 40\text{ N}\). Using Newton's second law, acceleration \(a = \frac{F}{m} = \frac{40}{2} = 20\text{ m/s}^2\).

By Newton's second law, \(F = \frac{\Delta p}{\Delta t} = \frac{mv}{t}\). Substituting the values, \(F = \frac{0.15\text{ kg} \times 20\text{ m/s}}{0.1\text{ s}} = 30\text{ N}\).

For complete mechanical equilibrium, a body must be in both translational equilibrium (net external force is zero) and rotational equilibrium (net external torque is zero).

Limiting friction is the maximum value of static friction (A \(\rightarrow\) Q). Static friction is a self-adjusting force (B \(\rightarrow\) R). Kinetic friction has a constant magnitude of \(\mu_k N\) (C \(\rightarrow\) P).

According to Newton's First Law, when the cloth is suddenly pulled, the dishes tend to maintain their state of rest due to the inertia of rest.

Assertion (A) is false. The Earth rotates and revolves, making a frame attached to it non-inertial. Reason (R) is false. Newton's laws in their original form are only valid in inertial frames. For a frame attached to the Earth, pseudo forces must be introduced to apply Newton's laws. Thus, both the Assertion and the Reason are false.

Assertion (A) is true. This is a fundamental statement of the Galilean principle of relativity. Reason (R) is true. The laws of physics are invariant in all inertial frames of reference. (R) correctly explains (A) because if physical laws are identical in all inertial frames, no internal experiment can distinguish between them.

Assertion (A) is true: To walk, a person pushes backward on the ground. By Newton's third law, the ground exerts a forward static friction force on the person's feet. This forward friction, combined with the normal force, creates a net force from the surface in the direction of motion, propelling the person forward.nReason (R) is false: For walking, the friction force exerted by the road on the person's feet is *in the direction* of the person's motion (forward friction), enabling propulsion. If friction were against the person's motion, walking would be impossible. Therefore, (A) is true but (R) is false.

Assertion (A) is true: If the elevator accelerates upwards, the apparent weight \(N = m(g+a)\) of the peanuts increases. If the moongphaliwala sells by the apparent weight reading (e.g., "1 kg" on the scale), they would be selling a *smaller actual mass* \(m_text{actual} = N/(g+a)\) for the same indicated weight. Thus, they gain more profit.

Reason (R) is true: When an elevator accelerates upwards, the normal force (apparent weight) on an object of mass \(m\) is \(N = m(g+a)\), which is greater than its actual weight \(mg\). Reason (R) correctly explains why the apparent weight increases, leading to the profit gain described in (A).

Assertion (A) is true: In an emergency, applying brakes in a straight line is generally a safer and more controlled maneuver to reduce speed and avoid collision, as sudden turns at high speed can lead to loss of control or skidding.

Reason (R) is true: Both stopping the car (through braking) and taking a turn (requiring centripetal force) on a horizontal road fundamentally rely on the friction force between the tires and the road. Reason (R) is true, but it does not explain *why* braking is preferred over turning; it merely states that friction is involved in both actions.

Therefore, (A) and (R) are true, but (R) is not the correct explanation of (A).