Two identical hollow spheres having mass m=3 kg and radius r=1 m are performing combined translational and rotational motion as shown in the figure. If ω=2 rad/s,vcom=3 m/s and ω′=3 rad/s,v′com=2 m/s, find the ratio of their kinetic energies.
A
37
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B
76
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C
87
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D
35
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Solution
The correct option is B76 Given, m=3 kg,r=1 m,ω=2 rad/s,vcom=3 m/s,ω′=3 rad/s,v′com=2 m/s
Moment of inertia of hollow sphere;I=23mr2=23×3×12=2 kg-m2.
Since, both sphere are identical therefore, I will be same.
We know that,
Total kinetic energy for combined translational and rotational motion is =12mv2COM+12Iω2 ⇒K.E=12mv2COM+12Iω2
So, for first sphere, K.E=12×3×32+12×2×22=17.5 J
Similarly, for other sphere K.E′=12mv′2com+12Iω′2 =12×3×22+12×2×32=15 J