In the figure shown, suppose the compound pulley and the disc have the same angular acceleration, in clockwise direction. If `a_1` is the upward acceleration of the compound pulley's centre (inner radius `r`, outer radius `3r`), `a_2` is the downward acceleration of the while `a_3` is the upward acceleration of the centre of the disc (radius `2r`). From kinematic constraints of the thread, the relation between them is:

Options

A. `a_(2)-(a_(3))/2=2a_(1)`
B. `a_(2)+a_(3)=(a_(1))/3`
C. `a_(2)-a_(3)=3a_(1)`
D. `a_(2)+2a_(3)=a_(1)`

Answer

A

Explanation

(the diagram for this solution is besides to the problem diagram).
At `A,a_(1)-ralpha=0.......(1)`
At `B,a_(B)=3ralpha-a_(1).......(2)`
or `a_(B)=2a_(1)`
`(a_(B)+a_(C))/(2)=a_(2)`
or `a_(C)=2a_(2)-2a_(1).......(3)`
From eqns. (3) and (4), we get `2a_(2)-a_(3)=4a_(1)`