A rigid body rotates about a fixed axis with variable angular velocity equal to `alpha-beta`, at the time t, where `alpha,beta` are constant. The angle through which it rotates before its stops

Options

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

Answer

A

Explanation

`omega = alpha - beta t` Comparing with `omega = omega_(0) - alpha t`
Initial angular velocity `= alpha`
Angular retardation `= beta`
`:.` Angular rotated before it stops `alpha^(2)`
`0=alpha^(2)-2 beta thetarArr theta =(alpha^(2))/(2beta)`.