1.

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 :

Answer»

`(A^(2))/(2B)`
`(A^(2)-B^(2))/(2A)`
`(A^(2)-B^(2))/(2B)`
`((A-B)A)/(2)`

Solution :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)`


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