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=√3gl5vcosθ=usinθ From conservation of energy, mglcosθ=2(12mu2)+12mv2 u=√2glcosθ2+tan2θ=√gl5, using θ=60∘ v=√3gl5

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