Question

If the applied torque is directly proportional to the angular displacement $\theta$, then the work done in rotating the body through an angle $\theta$ would be (C is constant of proportionality).

• A. C $\theta$
• B. $\frac{1}{2}$C$\theta$
• C. $\frac{1}{2}$ C ${\theta }^2$
• D. C ${\theta }^2$

Answer 1

The correct option is C $\frac{1}{2}$ C ${\theta }^2$

We know,

$W=\int \tau d\theta$

$\tau =c\theta$

$W=\int c\theta d\theta$

$W=\frac{c{\theta }^2}{2}$

Option $\text{C}$ is the correct answer