A metallic solid sphere is rotating about its diameter as axis of rotation. If the temperature is increased by `200^(@)C` the percentage increase in its moment of inertia is (Coefficient of linear expansion of the metal `= 10^(-5)//^(@)C`).

Options

A. `0.1%`
B. `0.2%`
C. `0.3%`
D. `0.4%`

Answer

D

Explanation

Coefficient of areal expansion ,
`beta = (A_(2) - A_(1))/(A_(1)(Delta t)`
` implies beta = (Delta R) /(R Delta t)`
` alpha = (Delta R)/(R Delta t) implies (Delta R)/ ( R ) = alpha Delta t `< br> Moment of inertia of solid sphere ,
` I = (2)/(3) MR^(2)`
`(Delta I)/(I) xx 100 = (2 Delta R)/(R) xx 100`
`= 2( alpha Delta t) xx 100`
=` 2 xx 10^(-5) xx 200 xx 100 `
0.4 %