Question

A cubical block of side $30cm$ 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:

• A. $13.3$
• B. $5.0$
• C. $9.4$
• D. $96.7$

Answer 1

The correct option is B $5.0$

Angular momentum of the block about the point O will be constant.

Hence,

$mvr=I\omega$

Moment of inertia about the point O = $\frac{m{a}^2}{6}+m(\frac{a}{\sqrt{2}}{)}^2$

$\omega =\frac{mvr}{I}$

After putting values:

$\omega =\frac{m\times 2\times 0.15}{2/3\times m\times a^2}$

$⟹\omega =5rad/s$