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Q.

A physical pendulum pivoted at a point executes angular oscillations. Its mass is m, has its centre of mass at distance r from the point of suspension. If its moment  of Inertia is  I, then its angular frequency is

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a

ω=MgrI2

b

ω=I2Mgr

c

ω=MgrI

d

ω=IMgr

answer is C.

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Detailed Solution

For a body executing simple harmonic motion, Restoring torque acting on it after a  small displacement θ, about an axis,
torque τ=cθ  here c=couple acting; θ is angular displacement  
We know that this results in angular oscillations which can be also related by the equation  torque=τ=Iα  ; here I=moment of inertia; α=angular acceleration
Equating the above two we get  cθ=Iα
Where for angular oscillations  α=ω2θ
Hence cθ=Iω2θ 
Simplifying this c=Iω2 
Hence  ω=cI
For angular oscillation ω=cI , where  ω=2πT
Restoring torque acting on a rod after a small displacement  θ, about an axis  passing through point of contact O with the curved path,
τ=Mgrsinθ=-r×F=force×perpendicular distance  , for small angles   sinθθ
Therefore,  τ=cθ=Mgrθ
Hence  c=Mgr. Substituting this is (1) we get 
ω=MgrI .
 

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A physical pendulum pivoted at a point executes angular oscillations. Its mass is m, has its centre of mass at distance r from the point of suspension. If its moment  of Inertia is  I, then its angular frequency is