A disc of mass m and radius r is gently placed on another disc of mass 2m and radius r. The disc of mass 2m is rotating with angular velocity `omega_(0)` initially.
The disc is placed such that axis of both are concident. The coefficient of friction is `mu` for surfaces of contact Assume that pressure on disc is uniformely distributed.

Angular velocity `'omega'` when both discs start rotating together without slipping

Options

A. `(2omega_(0))/(3)`
B. `(3omega_(0))/(4)`
C. `(omega_(0))/(3)`
D. `(omega_(0))/(2)`

Answer

B

Explanation

`V_(B)=omega(lcos30^(@))`
`V_(A)=omega(lsin30^(@))=V_(0)`
`implies omega=(2V_(0))/(l)`
`L_(ICR)=(I)_(ICR^(omega))`
`(I)_(ICR)=I_(cm)+md^(2)=(ml^(2))/(12)+m((l)/(2))^(2)=(ml^(2))/(3)`
`(I)_(ICR)=((ml^(2))/(3))((2v_(0))/(l))=(2mv_(0)l)/(3)`