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

Answer 1

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

Since, initially the body is at rest,

$\Rightarrow \omega =\alpha t=20t$

Given, $\frac{1}{2}I{\omega }^2=1200$
$\frac{1}{2}\times 1.5\times (20t{)}^2=1200$
$\therefore t=2\text{s}$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.