Question

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

Options

• 3 J

• 8 J

• 6 J

• 2 J

Answer 1

A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is 3 J.

Explanation:

Kinetic energy of rolling body is given by

`"K.E." =1/2"mv"^2(1+"k"^2/r^2)`

For a ring `k^2/r^2=1`

`therefore "K.E."_R=1/2"mv"^2(1+1)="mv"^2`

For a disc `k^2/r^2=1/2`

`therefore"K.E."_D=1/2"mv"^2(1+1/2)=3/4"mv"^2`

K.E._R = mv² = 4 J

`"K.E."_D=3/4"mv"^2=3/4xx4=3  "J"`