A thin uniform rod of length 2 l and mass M is acted upon a const… - Vidyadip

MCQ

A thin uniform rod of length $2 l$ and mass M is acted upon a constant torque. The angular velocity changes from zero to $\omega$ in time $t$. The value of torque is:

A
$\frac{M l^2 \omega}{3 t}$
B
$\frac{2 M l^2 \omega}{3 t}$
C
$\frac{M l^2 \omega}{12 t}$
D
$\frac{M l^2 \omega}{t}$

✓

Answer

(a) $\frac{M 2^2 \omega}{3 t}$
Explanation:
As Torque $(\tau)$ is equal to the product of Moment of Inertia (I) and Angular acceleration ( $\alpha$ )
$
\begin{aligned}
\tau & =I \alpha \\
\tau & =I \frac{\Delta \omega}{\Delta t} \\
\tau & =\left[\frac{M(2 l)^2}{12}\right]\left[\frac{\omega}{t}\right] \\
\tau & =\frac{M l^2 \omega}{3 t}
\end{aligned}
$

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