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A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

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By Expert Faculty of Sri Chaitanya
a
0
b
14
c
56
d
34
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detailed solution

Correct option is D

Conservation of Angular Momentum,  ⇒Iω+3I(0)=Iω1+3Iω1 ⇒ω4=ω1⇒Loss in Kinetic energy=Ki-Kf= 12Iω2−124Iω42=38Iω2⇒Fractional loss=Ki-KfKi=38Iω212Iω2=34


Similar Questions

A boy stands over the centre of a horizontal platform which is rotating freely with a speed of 2 revolutions/s about a vertical axis through the centre of the platform and straight up through the boy. He holds 2 kg masses in each of his hands close to his body. The. combined moment of inertia of the system is 1 kg×metre2. The boy now stretches his arms so as to hold the masses far from his body. In this situation, the moment of inertia of the system increases to 2kg×metre2. The kinetic energy of the system in the latter case as compared with that in the previous case will

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