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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 8 J, then K.E. of the disc is
  1. 2 J
  2. 16 J
  3. 4 J
  4. 6 J


Solution

The correct option is D 6 J
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=8 J
Hence from Eq (ii):
KEDisc=34mv2=34×8=6 J

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