When the temperature of a rod increases from t to `r+Delta t`, its moment of inertia increases from I to `I+Delta I`. If `alpha` is the value of `Delta I//I` is

Options

A. `2 alpha Delta T`
B. `alpha Delta T`
C. `(alpha Delta T)/(2)`
D. `(Delta T)/(alpha)`

Answer

A

Explanation

Moment of inertia of a rod, `I= (1)/(12) ML^(2)` …(i)
`:. Delta I = (1)/(12) 2 ML Delta L` ( `:.` M is a constant ) …(ii)
Divide (ii) by (i), we get `(Delta l)/(l) =2 (Delta L)/(L)` ..(iii)
As `Delta L= L alpha Delta T or (Delta L)/(L) = alpha Delta T`
Substituting the value `(Delta L)/(L)` in (iii), we get
`(Delta I)/(I) = 2 alpha Delta T`