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 inertia `I_(x)` and `l_(y)` is

Options

A. `I_(y) = 32 I_(x)`
B. `I_(y) = 16 I_(x)`
C. `I_(y) = I_(x)`
D. `I_(y) = 64 I_(x)`

Answer

D

Explanation

Mass of disc (X) , `m_(X) = pi R^(2) t rho`
where `rho` = density of material of disc.
`therefore I_(X) = (1)/(2) m_(X) R^(2) = (1)/(2) piR^(2) t rho R^(2)` or `I_(X) = (1)/(2) pi rho t R^(4)`
Mass of disc (Y) , `m_(Y) = pi (4R)^(2) (t)/(4) ""rho = 4 pi R^(2) t rho`
`therefore I_(Y) = (1)/(2) m_(Y) (4R)^(2) = (1)/(2) 4 pi R^(2) t rho (16R^(2)) = 32 pi t rho R^(4)`
`therefore (I_(Y))/(I_(X)) = (32 pi t rho R^(4))/((1)/(2) pi rho t R^(4)) = 64 or I_(Y) = 64 I_(X)`