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 $1500joule$, an angular acceleration of $25radian/se{c}^2$ must be applied about that axis for a duration of

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

Answer 1

The correct option is B $2seconds$

We know,

Kinetic rotational energy , $K=\frac{1}{2}I{\omega }^2$

$1500=\frac{1}{2}\ast 1.2\ast {\omega }^2$

Therefore, we get $\omega =50rad/s$

As body is initially at rest, ${\omega }_0=0$

Using rotational equation of motion,

$\omega ={\omega }_0+\alpha t$

50 =0 +25*t

t=2 seconds