Rotational Motion Question 211
Question: The moment of inertia of a body about a given axis is$1.2kgm^{2}$ . Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of$25radian/{{\sec }^{2}}$ must be applied about that axis for a duration of
Options:
A) 4 seconds
B) 2 seconds
C) 8 seconds
D) 10 seconds
Show Answer
Answer:
Correct Answer: B
Solution:
[b]
$ I=1.2 \mathrm{~kg} \mathrm{~m}^2, E_r=1500 J $
$ \alpha=25 \mathrm{rad} / \mathrm{sec}^2, \omega_1=0, t=\text { ? } $
$ A s E_r=\frac{1}{2} I \omega^2, \omega=\sqrt{\frac{2 E_r}{I}} $$ =\sqrt{\frac{2 \times 1500}{1.2}}=50 \mathrm{rad} / \mathrm{sec} $
$ \text { From } \omega_2=\omega_1+\alpha t $
$ 50=0+25 t, t=2 \text { seconds } $
