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Question

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



A
12340mv2
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B
23040mv2
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C
12340mv3
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D
12050mv2
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Solution

The correct option is A 12340mv2
Total energy= KEP1+KEP2+KEsphere ....(1)
calculation of kinetic energy of plates,

=12mv2+12m(2v)2=52mv2

Calculation for sphere,
KE=12Iω2+12mv2m
where, I=25mR2 for sphere.

let sphere moving with speed vcm
and ω=3v2R
v=Rωvcmv=R×3v2Rvcmvcm=v2
so the kinetic energy of sphere,

KE=12×25mR2(3v2R)2+12m(v2)2
KE=920mv2+mv28

So,finall kinnetic energy= 52mv2+KE=920mv2+mv28=12340mv2

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