CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


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
loader
B
a22b
loader
C
a24b
loader
D
a22b2
loader

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 answer



Physics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image