Explanation

(b) Let $R_{1}$ be the present distance between earth and sun and $T_{1}$ is duration of year. Let $R_{1}$ and $T_{2}$ be new values of distance and duration of year. By conservation of angular momentum we have
$I_{1}\omega_{1} = I_{2}\omega_{2}$,
or $\left( \frac{2}{5}MR_{1}^{2} \right)\frac{2\pi}{T_{1}} = \left( \frac{2}{5}mR_{2}^{2} \right)\frac{2\pi}{T_{2}}$
or $T_{2} = T_{1}\ \ \frac{R_{2}^{2}}{R_{1}^{2}}$
$= (365) \times \frac{(\frac{R_{1}}{2)}^{2}}{R_{1}^{2}}$
$= \frac{365}{4} = 91.25$ days
Hence, duration of year will become less.