Column I Column II (A) Body is a block lying on a rough inclined plane. Angle θ < angle of repose. A is inclined surface (P) Force exerted by A on body can be equal to it's weight in magnitude. (B) Body is a ball falling in liquid with terminal velocity. A is liquid. (Q) If density of body is somehow increased without changing r, it's state of motion (constant acceleration / constant velocity) or equilibrium position will be disturbed. (C) Body is a spherical ball rolling purely on inclined plane; inclined at an angle equal to angle of repose. The inclined surface is A. (R) Work done by the force exerted by A on the body is zero. (D) Body is m1 hanging on an ideal pulley system. A is string m1 < m2. (S) Mechanical energy of body is constant as time passes. (T) The kinetic energy of body is constant as time passes

Engineering

Physics

Motion of Block on Horizontal Surface

Static and Kinetic Friction

Motion of Block on Inclined Surface

Viscosity and Terminal Velocity New

Question

Column I	Column II
(A) Body is a block lying on a rough inclined plane. Angle θ < angle of repose. A is inclined surface	(P) Force exerted by A on body can be equal to it's weight in magnitude.
(B) Body is a ball falling in liquid with terminal velocity. A is liquid.	(Q) If density of body is somehow increased without changing r, it's state of motion (constant acceleration / constant velocity) or equilibrium position will be disturbed.
(C) Body is a spherical ball rolling purely on inclined plane; inclined at an angle equal to angle of repose. The inclined surface is A.	(R) Work done by the force exerted by A on the body is zero.
(D) Body is m₁ hanging on an ideal pulley system. A is string m₁ < m₂.	(S) Mechanical energy of body is constant as time passes.
	(T) The kinetic energy of body is constant as time passes

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This question involves matching physical scenarios (Column I) with possible outcomes (Column II). Each scenario describes a body interacting with a surface or medium (A), and we analyze forces, motion, and energy.

Key concepts:

(A) On an incline with θ < angle of repose, friction prevents sliding. The normal force from A is $m g \cos θ$ , which is less than weight mg, so (P) is false. Since it's at rest, work done by A is zero (R true), and mechanical energy is constant (S true).
(B) A ball falling in liquid at terminal velocity has zero acceleration. Force from A (viscous drag) equals weight (P true). Increasing density increases weight, disturbing terminal velocity state (Q true). Kinetic energy is constant (T true).
(C) A ball rolling purely on an incline at angle of repose moves with constant velocity. Friction does no work (R true), kinetic energy is constant (T true).
(D) In a pulley system with m₁ < m₂, m₁ accelerates upward. String force (A) does work, so mechanical energy isn't constant (S false).

Final matches: (A) - R,S; (B) - P,Q,T; (C) - R,T; (D) - None (since S is false and others don't apply).