A thin circular disc of mass 12 kg and radius 0.5 m rotates with an angular velocity of 100 rad/s. The rotational kinetic energy of the disc is

Options

A. 12.2 kJ
B. 5.5 kJ
C. 9. 2 kJ
D. 7.5 kJ

Answer

D

Explanation

Given mass of circular disc, M=12 kg, radius, R=0.5m,
angular velcoity, `omega=100rad//s`
`:.` Rotational kinetic energy of the disc,
`K=(1)/(2)Iomega^(2)`
`=(1)/(2).(1)/(2)MR^(2).omega^(2)" "[:'I=(1)/(2)MR^(2)]`
Putting the given values in the above relation,
`(1)/(4)xx12xx(0.5)^(2)xx100xx100`
`=7500J=7.5xx10^(3)5J=7.5kJ`
Hence, the rotational kinetic energy of the disc is 7.5 kJ