System Of Particles And Rotational Motion Ques 72

72. The moment of inertia of a body about a given axis is $1.2 kg m^{2}$. Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of $25 radian / sec^{2}$ must be applied about that axis for a duration of

[1990]

(a) 4 seconds

(b) 2 seconds

(c) 8 seconds

(d) 10 seconds

Show Answer

Answer:

Correct Answer: 72.(b)

Solution:

  1. (b) $I=1.2 kg m^{2}, E_r=1500 J$, $\alpha=25 rad / sec^{2}, \omega_1=0, t=$ ? As $E_r=\frac{1}{2} I \omega^{2}, \Rightarrow \omega=\sqrt{\frac{2 E_r}{I}}$

$=\sqrt{\frac{2 \times 1500}{1.2}}=50 rad / sec$

From $\omega_2=\omega_1+\alpha t$

$ 50=0+25 t, t=2 \text{ seconds } $

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