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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 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 mertia `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
Mass of disc `(X), mx = pi R^(2) t rho`
where `rho` = density of material of disc
:. `1_(X) = (1)/(2) m_(X) R^(2) = (1)/(2) R^(2) t rho R^(2)`
`1_(X) = (1)/(2) pi rho R^(4)`
Again mass of disc `(Y)`
`m_(y) = pi = (4 R)^(2) (t)/(4) rho = 4 pi R^(2) t rho`
and `I_(Y) = (1)/(2) m_(Y) (4R^(2)) = (1)/(2) 4 pi R^(2) t rho. 16 R^(2)`
`rArr I_(Y) = 32 pi t rho R^(4)`...(ii)
:. `(l_(y))/(l_(x)) = (32 pi t rho R^(4))/((1)/(2) pi rho t R^(4))`
`rArr = 64`
:. `1_(Y) = 64 1_(X)`.
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