Explanation

(b) Angular of the body is given by
$L = I\omega$
or $L = I \times \frac{2\pi}{T}\ or\ \ L \propto \frac{1}{T}$
$\Rightarrow$ $\frac{L_{1}}{L_{2}} = \frac{T_{2}}{T_{1}}$
$\frac{L}{L_{2}} = \frac{2T}{T}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $
$\ \ \ \ \ \ \ \ \ (As,\ T_{2} = 2T)$
So, $L_{2} = \frac{L}{2}$
Thus, on doubling the time period, angular momentum of body becomes half.