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Question

Two small rings, each of mass m, are connected to the block of same mass m through an inextensible massless string of length l. Rings are constrained to move over smooth rod AB. Initially, the system is held at rest as shown in Figure. Let u and v be the velocities of ring and block, respectively when string makes an angle 60 with the vertical.

A
u=gl5
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B
u=8gl5
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C
v=3gl
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D
v=3gl5
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Solution

The correct options are
A u=gl5
D v=3gl5
vcosθ=usinθ

From conservation of energy,
mglcosθ=2(12mu2)+12mv2
u=2glcosθ2+tan2θ=gl5, using θ=60
v=3gl5

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