A ring and a disc of same mass and radius roll without slipping along a horizontal surface with the same velocity. If the K.E. of the ring is 8J, then K.E. of the disc is
A
2J
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B
4J
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C
6J
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D
16J
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Solution
The correct option is C6J Let m be the mass and r be the radius for both objects ⇒Condition for rolling without slipping, v=rω KETotal=KERot+KETrans ⇒KETotal=12Iω2+12mv2...(i) Where v= translational velocity of COM of body I= Moment of inertia about axis passing through COM I=mr2 For ring I=mr22 For disc Total kinetic energy for disc: KEDisc=12×(mr22)×v2r2+12mv2 ⇒KEDisc=34mv2...(ii) Total kinetic energy for Ring: KERing=12×(mr2)×v2r2+12mv2 ∴KERing=mv2 ∵KERing=8J Hence from Eq (ii): KEDisc=34mv2=34×8=6J