Question

Moment of inertia of a body about a given axis is $1.5{\text{kg-m}}^2$. Initially the body is at rest. In order to produce a rotational kinetic energy of $1200\text{J}$, the angular acceleration of $20{\text{rad/s}}^2$ must be applied about the axis for a duration of

• A. $2\text{s}$
• B. $5\text{s}$
• C. $2.5\text{s}$
• D. $3\text{s}$

Answer 1

The correct option is A $2\text{s}$

Given: Moment of inertia $I=1.5{\text{kg-m}}^2$
Angular acceleration $;\alpha =20{\text{rad/s}}^2$
$K.E=\frac{1}{2}I{\omega }^2$
$1200=\frac{1}{2}\times 1.5\times {\omega }^2$
${\omega }^2=\frac{1200\times 2}{1.5}=1600$
$\omega =40\text{rad/s}$
$\omega ={\omega }_o+\alpha t$
$40=0+20t$
$t=2$ sec