Q88 / 90 · JEE Main 2016 (09 Apr Online) · Physics

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

A
13.3
Correct answer
B
5.0
C
9.4
D
6.7

Solution

Conservation of angular momentum about point

O

,

L_{before} = L_{after}

\Rightarrow m v R = I ω

\Rightarrow ω = \frac{m \times 2 \times [\frac{a}{2}]}{m [\frac{a^{2}}{6} + {(\frac{a}{\sqrt{2}})}^{2}]}

\Rightarrow ω = \frac{12}{8 a} = \frac{3}{2 \times 0 .3} = \frac{10}{2} = 5

rad s^{- 1}

Hence, the correct answer is option: 'B'.

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