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Newton's Laws for System of Particles

A rod of negl...

Question

A rod of negligible mass having length $l = 2 m$ is pivoted at its center and two masses, $6 kg$ and $4 kg$ are hung from the ends as shown in the figure. Find the initial angular acceleration of the rod if it is suddenly released from the horizontal position.

Take $g = 10 {m/s}^{2}$

2 {rad/s}^{2}

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3 {rad/s}^{2}

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4 {rad/s}^{2}

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5 {rad/s}^{2}

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Solution

The correct option is A $2 {rad/s}^{2}$

We know that,

$τ_{n e t} = I α$

$\Rightarrow m_{1} g (l / 2) - m_{2} g (l / 2) = [m_{1} (l / 2)^{2} + m_{2} (l / 2)^{2}] α$

$\Rightarrow 6 \times 10 \times (2 / 2) - 4 \times 10 \times (2 / 2) = [6 \times (2 / 2)^{2} + 4 \times (2 / 2)^{2}] α$

$\Rightarrow α = 2 {rad/s}^{2}$

Hence, option $(A)$ is the correct answer.

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