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

Answer

A

Explanation

Here `omega=(d theta)/(dt)=A-Bt`
`d theta=(A-Bt)dt`
When `omega=0,t=(A)/(B)`
Integrating `underset(0)overset(theta)intd theta=underset(0)overset(A//B)intAdt-underset(0)overset(A//B)intBtdt`
`theta=A[t]_(0)^(A//B)-B[(t^(2))/(2)]_(0)^(A//B)`
`=(AxxA)/(B)-B[(A^(2))/(2B^(2))]`
`=(A^(2))/(B)-(A^(2))/(2B)=(A^(2))/(2B)`