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 `I_(Y)` is :

Options

A. `I_(Y)=64I_(X)`
B. `I_(Y)=32I_(X)`
C. `I_(Y)=16I_(X)`
D. `I_(Y)=I_(X)`

Answer

A

Explanation

Now mass `=M="Vol"xxrho=piR^(2).t.rho`
M.I. of X is `I_(X)=(1)/(2)m_(1)R_(1)^(2).I_(X)=(1)/(2)piR^(2)rhot.R^(2).=(1)/(2)piR^(4)rhot" "...(i)`
`I_(Y)=(1)/(2)pi(4R^(2))xx(t)/(4)rho(4R)^(2)`
`=32piR^(4)rhot." "...(ii)`
`(I_(X))/(I_(Y))=(1)/(64)orI_(Y)=64I_(X)`.