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Question

Two plates 1 and 2 move with velocities v and 2v respectively. If the sphere does not slide relative to the plates, assuming the masses of each body as m, find the kinetic energy of the system (plate+sphere).


A
12540mv2
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B
12340mv2
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C
2390mv2
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D
2340mv2
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Solution

The correct option is B 12340mv2


In the above diagram, C is the point about which the whole body is rotating.
From the similar triangle we get,
yv=2Ry2v
y=23R

KE=12Icω2c
ω=vy=3v2R
Ic=25mR2+m(OC)2
OC=R3, as OC=(Ry)
Ic=2345mR2

KE=12(2345mR2)((32vR)2
KET=KE1+KE2+KEball
KET=12340mv2

For detailed solution watch next video.

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