A disc of mass 2 kg and radius 0.2 m is rotating about an axis passing through its centre and perpendicular to its plane with an angular velocity 50 rad/s . Another disc of mass 4 kg and radius 0.1m rotates about an axis passing through its centre and perpendicular to its plane with angular velocity 100 rad/s. If the two disc are coaxially coupled, then the angular velocity of coupled system would be

Options

A. 150 rad/s
B. 120 rad/s
C. 100/3 rad/s
D. 200/3 rad/s

Answer

D

Explanation

`I_(1)=(m_(1)r_(1)^(2))/(2)=(2xx0.04)/(2)=0.04kg m^(2)`
`I_(2)=(m_(2)r_(2)^(2))/(2)=(4xx0.01)/(2)=0.02 kg m^(2)`
`I_(1)omega_(1)+I_(2)omega_(2)=(I_(1)+I_(2))omega`
`therefore omega = (I_(1)omega_(1)+I_(2)omega_(2))/(I_(1)+I_(2))`
`=(0.04xx50+0.02xx100)/(0.04+0.02)`
`=(2+2)/(0.06)=(4xx100)/(6)`
`= (200)/(3)` rad/s.