A ring and a disc roll on the horizontal surface without slipping, with same linear velocity. If bolh have same mass and total kinetic energy of the ring is 4 J, then total kinetic energy of the disc is

Options

A. 3J
B. 4J
C. 5J
D. 6J

Answer

A

Explanation

Total KE of the rolling disc or ring is given by
`KE=1/2mv^2+1/2lomega^2` [Symbols have their usual meanings]
For ring and disc, translational kinetic energy will remain same, i.e. `1/2mv^2`
Rolling kinetic energy of the disc is `1/4mR^2omega^2`
Rolling kinetic energy of ring is `1/2mR^2omega^2`
As for ring, `4J=1/2mv^2+1/2mR^2omega^2`
For dics, `1/2mRomega^2+1/4mR^2omega^2 = (4/2+4/4)J=3J`