Question

The moment of inertia of a body about a given axis is $1.2\text{kg}\times {\text{m}}^2$. Initially, the body is at rest. In order to produce a rotational KE of 1500 joule, an angular acceleration of $25\frac{\text{rad}}{{\text{s}}^2}$ must be applied about that axis for a duration of

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

Answer 1

The correct option is B 2 seconds

$K_R=\frac{1}{2}I{\omega }^2=\frac{1}{2}I(\alpha t{)}^2=\frac{1}{2}I{\alpha }^2{t}^2$
$\Rightarrow 1500=\frac{1}{2}\times 1.2\times (25{)}^2{t}^2$
$\Rightarrow t^2=4\Rightarrow t=2\text{seconds}$
Hence, the correct answer is option (b).