The two particles of mass m and 2m, respectively are connected by a light rod of negligible mass and slide with negligible friction on a circular path of radius r on the inside of a fixed vertical cir

Question

The two particles of mass m and 2m, respectively are connected by a light rod of negligible mass and slide with negligible friction on a circular path of radius r on the inside of a fixed vertical circular ring. The system is released from rest at $θ = 0^{\circ}$ and $θ$ is taken from positive x-axis in clockwise direction, then :-

diagram

TestHub · Accepted Answer

Energy: v 2 = 3 2 g r ​ ( 2 sin θ + cos θ − 1 ) . Rod horizontal at θ = 4 5 ∘ : v = 3 2 g r ​ ( 2 ​ 3 ​ − 1 ) ​ - (A). Max speed at tan θ = 2 : v ma x ​ = 3 2 g r ​ ( 5 ​ − 1 ) ​ - (B), (C) wrong. v = 0 gives θ ma x ​ = 2 tan − 1 ( 2 ) - (D).

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