Question

$\huge\fbox\pink{@Siddhi163}$


A particle of mass m is rigidly attached at A to a ring of mass 3 m and radius r .The system is released from rest and rolls without sliding .The angular acceleration of ring just after release is?​

Answer 1

Answer:

$\bold{Moment \: of \: intertial \: of \: the \: system \: is}$

$\bold{I = {3mr}^{2} + {mr}^{2} = 4mr}^{2}$

$\bold{using \: τ=I∝= {4mr}^{2} ...(i)}$

$\bold{Torque \: by \: force \: around \: O \: is}$

$\bold{τ=mgr ...(ii)}$

$\bold{comparing (i) and (ii)}$

$\bold{∝ {4mr}^{2}=mgr}$

$\boxed{∝= \frac{g}{4r} }$

Note-:Refer to the attachment for diagram.

Answer 2

*Question:-

A particle of mass m is rigidly attached at A to a ring of mass 3 m and radius r .The system is released from rest and rolls without sliding .The angular acceleration of ring just after release is?

Answer:

$\bold{Moment \: of \: intertial \: of \: the \: system \: is}$

$\bold{I = {3mr}^{2} + {mr}^{2} = 4mr}^{2}$

$\bold{using \: τ=I∝= {4mr}^{2} ...(i)}$

$\bold{Torque \: by \: force \: around \: O \: is}$

$\bold{τ=mgr ...(ii)}$

$\bold{comparing (i) and (ii)}$

$\bold{∝ {4mr}^{2}=mgr}$

$\boxed{∝= \frac{g}{4r} }$

$\huge\fbox\green{@Shwetasingh1421977}$