Two discs, each having moment of inertia `5 kg m^(2)`. about its central axis, rotating with speeds `10 rad s^(-1)` and `20 rad s^(-1)`, are brought in contact face to face with their axes of rotation coincided. The loss of kinetic energy in the process is

Options

A. `2J`
B. `5J`
C. `125J`
D. `0J`

Answer

C

Explanation

Applying conservation of angular mometum,
`(5+5)omega'=5xx10+5xx20=150`
or `omega'=15 rads^(-1)`
Initial kinetic energy
`=1/2xx5xx10x10+1/2xx5xx20xx20`
`=250+1000=1250J`
Final kinetic enegy `=1/2xx10xx15xx15=1125J`
Loss of kinetic energy `=(1250-1125)J=125J`