System Of Particles And Rotational Motion Ques 47

47. A constant torque of $1000 $ $N-m$ turns a wheel of moment of inertia $200$ $ kg-m^{2}$ about an axis through its centre. Its angular velocity after $3$ seconds is

[2001]

(a) $1$ $ rad / s$

(b) $5$ $ rad / s$

(c) $10$ $ rad / s$

(d) $15$ $ rad / s$

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Answer:

Correct Answer: 47.(d)

Solution:

  1. (d) $\tau=1000$ $ N-m, I=200 $ $kg-m^{2}$

$\tau=I . \alpha$ and $\alpha=(\frac{\omega_f-\omega_0}{t})$

$\Rightarrow \alpha=\frac{1000}{200}=5$ $ rad / sec^{2}$

$\omega_1=\omega_0+\alpha t=0+3 \times 5=15$ $ rad / s$

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