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  4. A cubical block of side 30 cm is moving with velocity 2 ms-1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

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Q. A cubical block of side $30\,cm$ is moving with velocity $2 \, ms^{-1}$ on a smooth horizontal surface. The surface has a bump at a point $O$ as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :Physics Question Image

JEE MainJEE Main 2016System of Particles and Rotational Motion

Solution:

$mv=I\omega$
$\omega=\frac{m\cdot2 \frac{R}{2}}{m\left[\frac{R^{2}}{6}+\left(\frac{R}{\sqrt{2}}\right)^{2}\right]}$
$\omega=\frac{12}{8R}=\frac{3}{2\times0.3}=\frac{10}{2}=5$