A rigid body rotates about a fixed axis with variable angular speed `omega=A-Bt` where A and B are constant. Find the angle through which it rotates before it comes to rest :

Options

A. `(a^(2))/(2b)`
B. `(a^(2)-b^(2))/(2ab)`
C. `(a^(2)-b^(2))/(2b)`
D. `(a^(2)-ab)/(2a)`

Answer

A

Explanation

Here we have `omega=a-bt`
At `t=0, omega=omega_(0)`
`omega_(0)=a`
Also `alpha=(domega)/(dt)=-b`
Applying `omega^(2)-omega_(0)^(2)=2alphatheta`
or `0=a^(2)+2(-b).theta`
or `2btheta=a^(2)`
or `theta=(a^(2))/(2b)`