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A circular disc X of radius R is made fr...

A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness `(t)/(4)`. Then the relation between the moment of inerita `I_X` and `I_Y` is

A

`I_(Y) = 32 I_(X)`

B

`I_(Y) = 16 I_(X)`

C

`I_(Y)= I_(X)`

D

`I_(Y) = 64 I_(X)`

Text Solution

Verified by Experts

The correct Answer is:
D
Mask of disck X, `m_(x) = piR^(2)trho`, where `rho` is the density of the material of the disc.
`therefore I_(N) = 1/2m_(x)R^(2) =1/2piR^(2)trho R^(2) = 1/2pi rho tR^(4)`
Mass of disc, Y,
`m_(y) = pi(4r)^(2) t/4 rho =4pi R^(2) trho therefore I_(Y) = 1/2m_(y)(4R)^(2)=1/24piR^(2)trho xx 16 R^(2) = 32pi t rho R^(2) rArr I_(Y) = 64 I_(X)`
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