System of Particles and Rotational Motion - Result Question 52

56. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω1 and ω2. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is:-

[2017]

(a) 14I(ω1ω2)2

(b) I(ω1ω2)2

(c) 18(ω1ω2)2

(d) 12I(ω1+ω2)2

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Answer:

Correct Answer: 56. (a)

Solution:

  1. (a) Here, Iω1+Iω2=2Iω

ω=ω1+ω22

(K.E)i=12Iω12+12Iω22

(K.E. )f=12×2Iω2=I(ω1+ω22)2

Loss in K.E. =(K.E)f(K.E)i=14I(ω1ω2)2



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