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Q.

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:

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a

6.7

b

5.0

c

9.4

d

13.3

answer is B.

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Detailed Solution

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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=mvr=mva2
Also, after hitting point O, L=Iω
2. Using conservation of angular momentum,  mva2=Iω
3. Moment of inertia (I) of cubical block about one edge is given by
I=ma26+a22 
ω=m.2a2ma26+a22 
ω=128a=32×0.3=102=5 rad/sec 
Therefore, the correct answer is (B).
 

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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: