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Question

A disc of mass 1 kg and radius 0.1 m is rotating with angular velocity 20rad/s. What is angular velocity (in rad/s) if a mass of 0.5 kg is put on the circumference of the disc?

A
10
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B
20
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C
40
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D
30
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Solution

The correct option is A 10
Initial angular velocity is ω1=20 rad/s
Moment of Inertia of disc is I1=mr2/2=1×0.012kgm2=0.005kgm2
The new moment of inertia when a particle is placed on the circumference i.e at a distance r from the axis is , I2=I1+Mr2=0.005+0.5kg×(0.1)2=0.01kgm2
In this process the the angular momentum, J=Iω will remain conserved so I1ω1=I2ω2
so the new angular velocity, ω2=I1I2ω1=0.0050.0120=10rad/s

Option A is correct.

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