Question

Moment of inertia of a body about an axis is $4kg{m}^2$. The body is initially at rest and a torque of $8Nm$ starts acting on it along the same axis. Work done by the torque in $20s$, in joules, is :

• A. $40$
• B. $640$
• C. $2560$
• D. $3200$

Answer 1

The correct option is D $3200$

Angular acceleration of the body will be $\alpha =\frac{8}{4}=2rad/s^2$.

Angular velocity in 20s will be $\omega =2\left(20\right)=40rad/s$.

Since by work energy theorem, work done is equal to the change in kinetic energy,

$W=\frac{1}{2}4\left({40}^2\right)-0=3200J$.