Two discs of same moment of inertia rotating about their respective geometrical 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
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a
14I(ω1-ω2)2
b
I(ω1-ω2)2
c
18I(ω1-ω2)2
d
12I(ω1+ω2)2
answer is A.
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Detailed Solution
Common angular veocity ω is given , Iω1 + Iω2 = 2Iω ⇒ ω = ω1+ω22(K.E.)i = 12Iω12+12Iω22(K.E.)f = 12×(2I)ω2 = I(ω1+ω22)2Loss in K.E. = (K.E.)i-(K.E.)f = I4(ω1-ω2)2