First slide

Rotational motion

Question

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

Moderate

A

13.3
B

5.0
C

9.4
D

6.7

Solution

1.
Given Side of block $a = 30 cm=0.3 m$
Velocity $v = 2 m / s$
Before hitting point O ,We know angular momentum $L = m v r = m v \frac{a}{2}$
Also, after hitting point O, $L = I ω$
2. Using conservation of angular momentum, $m v \frac{a}{2} = I ω$
3. Moment of inertia (I) of cubical block about one edge is given by
$I = m (\frac{a^{2}}{6} + {(\frac{a}{\sqrt{2}})}^{2})$
$∴ ω = \frac{m .2 \frac{a}{2}}{m [\frac{a^{2}}{6} + {(\frac{a}{\sqrt{2}})}^{2}]}$
$\Rightarrow ω = \frac{12}{8 a} = \frac{3}{2 \times 0.3} = \frac{10}{2} = 5 rad / sec$
Therefore, the correct answer is (B).

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