Answer the following by appropriately matching the lists based on the information given in the paragraph. One end of an ideal string is connected with a point mass of mass m and the other end is conne

Question

Answer the following by appropriately matching the lists based on the information given in the paragraph. One end of an ideal string is connected with a point mass of mass m and the other end is connected with a fixed point O. A ball can move in vertical circle. At the lowest point, speed of ball is v.

List - I	List - II
(I) $v = g ℓ$	(P) Speed at B is $g ℓ$ .
(II) $v = 2 g ℓ$	(Q) Speed at B is $2 g ℓ$ .
(III) $v = 3 g ℓ$	(R) Speed at B is zero
(IV) $v = 4 g ℓ$	(S) Particle completes circular motion.
	(T) Particle does not complete circular motion.

TestHub · Accepted Answer

Completing the circle needs v ≥ 5 g ℓ ​ ; reaching B needs v ≥ 2 g ℓ ​ , with v B ​ = v 2 − 2 g ℓ ​ . v = g ℓ ​ : the ball oscillates and never completes the circle (I → T). v = 2 g ℓ ​ : v B ​ = 0 (II → R, T). v = 3 g ℓ ​ : v B ​ = g ℓ ​ (III → P, T). v = 4 g ℓ ​ : v B ​ = 2 g ℓ ​ (IV → Q, T). Option (B).

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