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JEE Main 2019 (10 Jan, Shift 2) · Rotational Kinematics & Dynamics

Rotational Kinematics & Dynamics question from JEE Main 2019 (10 Jan, Shift 2)

Q56JEE Main 2019 · 10 JAN · SHIFT 2Medium

Rotational Kinematics & Dynamics

A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be -

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Answer: (a)

Torques about P: $5M_0$ at $l$ on one side, $2M_0$ at $2l$ on the other.
Net $\tau = 5M_0gl - 2M_0g(2l) = M_0gl$
$I = 5M_0l^2 + 2M_0(2l)^2 = 13M_0l^2$
$\alpha = \frac{\tau}{I} = \frac{g}{13l}$
So the answer is (a) $\frac{g}{13l}$ .

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