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Q.

A small block of mass m is rigidly attached at ‘P’ to a ring of mass m and radius r. The system is released from rest at $θ = 30 °$ and rolls without sliding. The speed of centre of mass of system when block reaches the bottom is

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a

none

b

$\sqrt{\frac{rg}{2}}$

c

$\frac{\sqrt{rg}}{2}$

d

$\sqrt{rg}$

answer is D.

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Detailed Solution

Apply work energy $\frac{mgr}{2} = \frac{1}{2} (2 {mr}^{2}) ω^{2}$
$ω = \sqrt{\frac{g}{2 r}} \Rightarrow V_{cm} = \frac{ωr}{2} = \sqrt{\frac{gr}{8}}$

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A small block of mass m is rigidly attached at ‘P’ to a ring of mass m and radius r. The system is released from rest at θ=30° and rolls without sliding. The speed of centre of mass of system when block reaches the bottom is