A rough disc of mass `m` rotates freely with an angular velocity `omega`. If another rough disc of mass `m/2` and same radius but spinning in opposite sense with angular speed `omega` is kept on the first disc. Then:

Options

A. the final angular speed of the dise is `omega/3`
B. the net work does by friction is zero
C. the friction does a positive work on the lighter disc
D. the net work done by friction is `(-mR^(2)omega^(2))/3`

Answer

A, D

Explanation

`1/2 mr^(2)xxomega-1/2 m/2 r^(2)xx omega=(1/2 mr^(2)+1/4mr^(2))omega'`
`rArromega'=omega//3`
d) use work energy principle
`w_(f)+w_(g)=Delta(DE)rArr1/2 (3/4 mr^(2)) omega^(2)//9`
`-[1/4mr^(2)omega^(2)+1/8 mr^(2) omega^(2)]`
`rArrw_(f)+0=-m(omega^(2)r^(2))/3`