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 B12340mv2
In the above diagram, C is the point about which the whole body is rotating.
From the similar triangle we get, yv=2R−y2v ⇒y=23R
KE=12Icω2c ω=vy=3v2R Ic=25mR2+m(OC)2 ⇒OC=R3, as OC=(R−y) Ic=2345mR2