Question

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

• A. 2s
• B. 5s
• C. 2.5 s
• D. 3s

Answer 1

Answer: (A)

Given moment of inertia 'I' = 1.5 kgm${}^2$
Angular Acc. "a" = $20Rad/s^2$
$KE=\frac{1}{2}I{\omega }^2$
$1200=\frac{1}{2}1.5\times {\omega }^2$
${\omega }^2=\frac{1200\times 2}{1.5}=1600$
$\omega =40\text{rad}/s^2$
$\omega ={\omega }_0+\alpha t$
$40=0+20t$
$t=2\sec$