A large disc has mass 2kg and radius 0.2 m and initial angular velocity 50 rad/s and small disc has mass 4kg and radius 0.1 m and initial angular velocity 200 rad/s both rotating about their common axis. Then the common final angular velocity after discs are in contact is,

Options

A. 40
B. 60
C. 100
D. 120

Answer

C

Explanation

Give: `m_(1)=2kg" "m_(2)=4kg`
`r_(1)=0.2m" "r_(2)=0.1m`
`w_(1)=50" rad s"^(-1)" "w_(2)=200" rad s"^(-1)`
As, angular momentum, `I_(1)W_(1)=I_(2)W_(2)` = Constant
`thereforeW_(f)=(I_(1)W_(1)+I_(2)W_(2))/(I_(1)+I_(2))=((1)/(2)m_(1)r_(1)^(2)w_(1)+(1)/(2)m_(2)r_(2)^(2)w_(2))/((1)/(2)m_(1)r_(1)^(2)+(1)/(2)m_(2)r_(2)^(2))`
By putting the value of `m_(1),m_(2),r_(1),r_(2)` and solving we get = 100 rad `s^(-1)`