PYQ NEET- Rotational Motion L-2

Question: A constant torque of $100 \mathrm{~N} \mathrm{~m}$ turns a wheel of moment of inertia $300 \mathrm{~kg} \mathrm{~m} 2$ about an axis passing through its centre. Starting from rest, its angular velocity after $3 \mathrm{~s}$ is :-#

A) $1 \mathrm{rad} / \mathrm{s}$

B) $5 \mathrm{rad} / \mathrm{s}$

C) $10 \mathrm{rad} / \mathrm{s}$

D) $15 \mathrm{rad} / \mathrm{s}$

Answer: $1 \mathrm{rad} / \mathrm{s}$#

Solution:#

$\begin{aligned} \tau & =\mathrm{I} \alpha \Rightarrow \alpha=\frac{\tau}{\mathrm{I}}=\frac{100}{300}=\frac{1}{3} \mathrm{rad} / \mathrm{sec}^2 \ \omega_{\mathrm{i}} & =0 \ \omega_{\mathrm{f}} & =\omega_{\mathrm{i}}+\alpha \mathrm{t} \ & =0+\frac{1}{3} \times 3 \ \omega_{\mathrm{f}} & =1 \mathrm{rad} / \mathrm{sec}\end{aligned}$