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

Options

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

Answer

A

Explanation

Total KE of the rolling disc or ring is given by
`KE=(1)/(2)mv^(2)+(1)/(2)l omega^(2)`
For ring and disk, translational kinetic energy `(1)/(2)mv^(2)` is constant.
Rolling KE of disc is `(1)/(4)mR^(2)omega^(2)`
Rolling KE of ring is `(1)/(2)mR^(2)omega^(2)`
`"As for ring, "4J=(1)/(2)mv^(2)xx(1)/(2)mR^(2)omega^(2)`
`therefore" "mR^(2)omega^(2)=4J`
For `"disc"(1)/(2)mR^(2)omega^(2)+(1)/(4)mR^(2)omega^(2)`
`=((4)/(2)+(4)/(4))J=(2+1)J=3J`