Two discs of moment of inertia I1 and I2 and angular speeds ω1 and ω2 are rotating along collinear axes passing through their center of mass and perpendicular to their plane. If the two are made to rotate together along the same axis the rotational KE of system will be
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a
I1ω1+I2ω22I1+I2
b
I1+I2ω1+ω222
c
I1ω1+I2ω222I1+I2
d
None of these
answer is C.
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Detailed Solution
By the law of conservation of angular momentum, I1ω1+I2ω2=I1+I2ωAngular velocity of system, ω=I1ω1+I2ω2I1+I2Rotational kinetic energy=12I1+I2ω2=12I1+I2I1ω1+I2ω2I1+I22=I1ω1+I2ω222I1+I2