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Question

A cubical block of side 10 cm is moving with velocity 20 cm/s on a horizontal smooth plane as shown. It hits a ridge at point O as shown in the figure. What is the angular speed of the block after it hits O?


A
3.5 rad/sec
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B
3 rad/sec
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C
2 rad/sec
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D
1.5 rad/sec
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Solution

The correct option is D 1.5 rad/sec
Given that
Side of cubical block (a)=10 cm
Speed of block (v)=20 cm/s
Distance OM =r=102 cm


Net torque about O is zero, so angular momentum about O will be conserved.
Initial angular momentum (Li)=mv×a2
Final angular momentum Lf=I0ω
mva2=(Icm+mr2)ω (r2=a22)
mva2=(ma26+m(a22))ω
mva2=23ma2ω
ω=3v4a
ω=3×204×10
ω=1.5 rad/s

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