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Question

A uniform disk (m = 2 kg, r = 50 cm) is rotating at an angular speed 480 rpm. A second disk (m = 1 kg, r = 160 cm) is rotating at speed 360 rpm. Now first disk is dropped gently on second disk & they eventually rotate together about common axis. Find final angular velocity in rad/s.

A
12.6 π
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B
11.2π
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C
22.4 π
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D
6.4 π
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Solution

The correct option is A 12.6 π

L1=I1ω1
L2=I2ω2 Lsystem=I1ω1+I2ω2
At equilibrium

L′′=(I1+I2)ω
Now L1+L2=L′′
ω=I1ω1+I2ω2I1+I2

ω1=480 rpm=16π rad/s
ω2=360 rpm=12π rad/s
I1=12×2×0.52=0.25 kgm2I2=12×1×1.62=1.28 kgm2
Substitute the values to get, ω=12.6π rad/s

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