Question

# A rigid body rotates about a fixed axis with variable angular velocity equal to (a-bt) at time t where a and b are constants. The angle through which it rotates before it comes to rest is___?

A
a2b
B
a22b
C
a24b
D
a22b2

Solution

## The correct option is B $$\dfrac{a^2}{2b}$$Let the angle rotated be $$\theta$$Given,$$\omega=a-bt$$$$\dfrac{d\theta}{dt}=a-bt$$Also,It will come to rest when, $$\omega=a-bt=0$$$$t_f=\dfrac{a}{b}$$$$\displaystyle \int_0^\theta d\theta=\int_0^{\dfrac{a}{b}} a-bt$$$$\theta=\dfrac{a^2}{b}-\dfrac{a^2}{2b}=\dfrac{a^2}{2b}$$Option $$\textbf B$$ is the correct answerPhysics

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