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Angular Impulse

A small block...

Question

A small block of mass ‘m’ is rigidly attached at ‘P to a ring of mass ‘3m’ and radius ‘r’. The system is released from rest at $θ$ = $90^{0}$ and rolls without sliding. The angular acceleration of hoop just after release (about the centre of the ring) is

A

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B

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C

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D

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Solution

The correct option is B

$\sum F = m a \Rightarrow f = 4 m a . . (1) A b o u t t h e c e n t e r τ = I = α \Rightarrow (m g - f) r = (3 m r^{2} + m r^{2}) a o r m g - f = 4 m a . . . (2) F r o m (1) a n d (2) 8 m a = m g a = \frac{g}{g} a = \frac{g}{8 r}$

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