Question

The moment of inertia of a body about a given axis is 1.2 kg $m^2$. Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 $rad/s^2$ must be applied about that axis for a duration of

• A. 4 s
• B. 2 s
• C. 8 s
• D. 10 s

Answer 1

The correct option is B 2 s

$KE=\frac{I{\omega }^2}{2}$

$1500=\frac{1.2\times {\omega }^2}{2}\to \omega =50$

${\omega }_o=0$

$\omega ={\omega }_o+\alpha t=25t=50$

$t=2sec$