A particle of mass 1 kg is released from rest at point A as shown, a vertical distance h 1 above the ground. It slides down an inclined track, around a circular loop of radius R , then up another in

Question

A particle of mass 1 kg is released from rest at point A as shown, a vertical distance $h_{1}$ above the ground. It slides down an inclined track, around a circular loop of radius R , then up another incline that forms an angle of 45° with the horizontal. The block slides off the track at point C , which is at height R above the ground. Assume the entire track to be frictionless. At point D normal contact force is 22 N and velocity of the particle is $12 m / s$ . Then :

List - I	List - II
(P) $h_{1}$	(1) $\frac{39}{40}$
(Q) R	(2) $\frac{3}{8}$
(R) $h_{2}$	(3) $\frac{27}{20}$
(S) $x_{0}$	(4) $\frac{69}{80}$
	(5) None of these

TestHub · Accepted Answer

P: loop completion, energy: h 1 ​ = 20 27 ​ m. Matches (3). Q: loop top N + m g = R m v 2 ​ ; energy: R = 8 3 ​ m. Matches (2). R: projectile after C: h 2 ​ = 80 69 ​ m. Matches (4). S: horizontal range x 0 ​ = 40 39 ​ m. Matches (1). P-3, Q-2, R-4, S-1. Answer: (B).

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