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Question

A disc of mass 2kg and radius 0.2m is rotating with angular velocity 39rad s−1. What is angular velocity, if two masses each of 0.25kg is put on periphery of the disc?

A
24rad s1
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B
36rad s1
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C
15rad s1
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D
26rad s1
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Solution

The correct option is A 24rad s1
Angular momentum in absence of any external torque remains constant. If no external torque acts on a system of particles, then angular momentum of the system remains constant,
i.e,τ=0dLdt=0L=Iω=constant
Initial angular momentum = Final angular momentum
I1ω1=I2ω2
12Mr2ω1=12(M+2m)r2ω2...(i)

Here, M=2kg,m=0.25kg,r=0.2m,ω1=30rad/s
Hence, we get after putting the given values in Eq.(i)
12×2×(0.2)2×30=12×(2+2×0.25)(0.2)2×ω2
1.2=0.05ω2ω2=24rad/s



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