There are five mechanical setups as shown in column along with respective free body diagrams of the block. In each free body diagram force represented have magnitude proportional to length of arrows.

Question

There are five mechanical setups as shown in column along with respective free body diagrams of the block. In each free body diagram force represented have magnitude proportional to length of arrows. In each case block is at rest initially. If block begins to move in any situation then only consider the situation after starting of motion. Match List-I with List-II.

List - I	List - II
(P) $F_{1} + F_{2} = 0$	(1) Boy pulling a block on a rough surface.
(Q) $F_{1} + F_{2} + F_{3} + F_{4} = 0$	(2) A spring block system placed on a rough surface.
(R) $F_{1} + F_{2} + F_{3} + F_{4} = m a$ with $∣ a ∣ \neq = 0$	(3) Block placed on a rough incline and pushed downward.
(S) $F_{3}$ is static friction.	(4) Block being pushed on a rough horizontal surface. (Consider horizontal projection of $F_{4}$ = magnitude of $F_{3}$ )
	(5) Block being pulled on a rough horizontal surface. (Consider horizontal projection of $F_{4}$ = magnitude of $F_{3}$ and the block is not leaving the contact with the floor)

TestHub · Accepted Answer

In every free body diagram: F1 = normal reaction, F2 = weight, F3 = friction, F4 = applied/spring force.

(P) $F_{1} + F_{2} = 0$ : in setups (1) and (2) the applied force is horizontal, so N = mg and the vertical pair cancels. In (3), (4), (5) the applied force has a vertical component (incline, push-down, pull-up), so N ≠ mg. → 1, 2

(Q) $F_{1} + F_{2} + F_{3} + F_{4} = 0$ : in setups (4) and (5) the horizontal projection of F4 equals F3 (given), so horizontal forces cancel and vertical forces balance; the block stays at rest. → 4, 5

(R) $F_{1} + F_{2} + F_{3} + F_{4} = m a$ : in setups (1), (2), (3) the driving force exceeds friction, so the block accelerates. → 1, 2, 3

(S) F3 is static friction: in setups (4) and (5) the block does not move, so friction is static; in (1), (2), (3) the block slides (kinetic friction). → 4, 5

Hence P→1,2; Q→4,5; R→1,2,3; S→4,5, option (B).

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