Angular of the body is given by

$L=I\omega$

or $L=I\times \frac{2\pi }{T} \mathrm{o}\mathrm{r} L\propto \frac{1}{T}$

$\Rightarrow$ $\frac{L_1}{L_2}=\frac{T_2}{T_1}$

$\frac{L}{L_2}=\frac{2T}{T}$

$(As, T_2=2T)$

So, $L_2=\frac{L}{2}$

Thus, on doubling the time period, angular momentum of body becomes half.