A drum of mass `m_(1)` and radius `r_(1)` rotates freely with initially angular velocity `omega_(0)`. A second drum with mass `m_(2)` and radius `r_(2)(r_(2)gtr_(1))` is mounted on same axle and is at rest although it is free to rotate. A thin layer of sand with mass `m` is distributed on iner surface of smaller drum. At `t=0` small perforations in the inner drum are opened. The sand starts to fly out at a consant rate `lamdakg//sec` and sticks to the outer drum. Ignore the transit time of the sand. Choose the corect alternatives.

Options

A. Angular speed of outer drum at time is `(lamda t omega_(0))/(m_(2)+lamdat)((r_(1))/(r_(2)))^(2)`
B. Difference in final angular speeds of two drums is 0
C. Difference in final angular speeds of two drums is `((m(r_(2)^(2)-r_(1)^(2))+m_(2)r_(2)^(2))/((m+m_(2))r_(2)^(2)))omega_(0)`
D. Angular speed of inner drum remains constant

Answer

A, C, D

Explanation

As the sand leaves the inner drum through the open holes, it does not exert any force of the drum, angular momentum remains conserved.
At time `t`,
`m_(1)r_(1)^(2)omega_(0)=(m_(1)-lamdat)r_(1)^(2)omega_(0)+(m_(2)+lamdat)r_(2)^(2) omega_(2)`
`omega_(2)-(lamdat r_(1)^(2)omega_(0))`
`((m_(2)+lamdat)r_(2)^(2))`
The speed of inner drum does not change.