A loop and a disc have same mass and roll without slipping with the same linear velocity `v`. If the total kinetic energy of the loop is `8 J`, the kinetic energy of the disc must be.

Options

A. `8J`
B. `6J`
C. `16J`
D. `4J`

Answer

B

Explanation

Total kinetic energy of loop
`=1/2mv^(2)+1/2lomega^(2)`
`=1/2mv^(2)+1/2(mr^(2))(v^(2))/(r^(2))=mv^(2)=8`
Again total kinetic energy of disc
`=1/2mv^(2)+1/2lomega^(2)=1/2mv^(2)+1/2xx1/2mr^(2)xx(v^(2))/(r^(2))`
`=1/2mv^(2)+1/4mv^(2)=3/4mv^(2)=3/4xx8J=6J`