Question

If radius of earth becomes $n$ times its present value, without change in mass, then duration of day becomes.

Answer 1

By conservation of angular momentum ,

$\Rightarrow I_1{w}_{=}{I}_2{w}_2$

$\frac{2}{5}M{R}^2\times \frac{2\pi }{24hour}=\frac{2}{5}M{\left(nR\right)}^2\frac{2\pi }{T}$

$\Rightarrow T=n^{2}24h$

Hence, the answer is $n^{2}24h.$