When the temperature of a body increases from `T to T+ DeltaT`, its moment of inertia increases from `I to I + DeltaI`. If `alpha` is the coefficient of linear expansion of the material of the body, the `(Delta I)/(I)`is (neglect higher order of `alpha`)

Options

A. `alpha DeltaT`
B. `2alphaDeltaT`
C. `(DeltaT)/(alpha)`
D. `(2a)/(DeltaT)`

Answer

B

Explanation

`I = mK^(2)`
`log I = log (mK^(2))`
On differentiating, we get,
`implies (DeltaI)/(I)=0+2 (DeltaK)/(K)`
`therefore (DeltaI)/(I) = 2 alpha DeltaT`