Question

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

• A. $4s$
• B. $2s$
• C. $8s$
• D. $10s$

Answer 1

The correct option is B $2s$

As kinetic energy is given as $E=\frac{I{\omega }^2}{2}$,

for $E=1500J,I=1.2kg{m}^2$ angular velocity $\omega =\sqrt{1500\times 2/1.2}=\sqrt{2500}=50rad/s$

$\alpha =\omega \times t$

So duration of time for which torque should be applied is $\omega /\alpha =50/25=2s$