Disc of mass M=10 kg and radius R=50 cm is revolving about fixed vertical axis on smooth horizontal surface with angular velocity `omega_(0)=10 rad//s`. A block of mass m=5kg is connected throgh disc through slack string as shown in the diagram. Find the angular velocity (in rad/s) when string becomes taut.

Answer

3

Explanation

`1/2 xxMxxR^(2) omega_(0) =1/2 MR^(2) omega+mvR`
`v=R omega`
`rArr 1/2 M omega_(0)=(1/2 M+m) omega`
`omega=(Momega_(0))/(M+2m) =(10xx10)/(10+10) =5 rad//s`