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Question

Physics Question on System of Particles & Rotational Motion

A circular disc XX of radius RR is made from an iron pole of thickness tt, and another disc Y of radius 4R4R is made from an iron plate of thickness t4\frac {t}{4}. then the relation between the moment of inertia IXI_X and IYI_Y is

A

Iy=32IxI_y=32I_x

B

Iy=16IxI_y=16I_x

C

Iy=32IxI_y=32\,I_x

D

Iy=64IxI_y=64\,I_x

Answer

Iy=64IxI_y=64\,I_x

Explanation

Solution

If t is the thickness and R is the radius of the disc, then mass =pR2t?= pR^2t? ?=? = density of the material of the disc. Moment of inertia of disc X, Ix=12πR4tρ...(i)I_{x}=\frac{1}{2}\pi R^{4}t\rho\,...\left(i\right) Moment of inertia of disc Y, Iy=32πR4tρ...(ii)I_{y}=32\,\pi R^{4}t\rho\,...\left(ii\right) From equation (i)\left(i\right) and (ii)\left(ii\right) Iy=64IxI_{y}=64\,I_{x}