Question

A rod of negligible mass having length $l=2\text{m}$ is pivoted at its center and two masses, $6\text{kg}$ and $4\text{kg}$ 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 $g=10{\text{m/s}}^2$

• A. $2{\text{rad/s}}^2$
• B. $3{\text{rad/s}}^2$
• C. $4{\text{rad/s}}^2$
• D. $5{\text{rad/s}}^2$

Answer 1

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


We know that,

${\tau }_{net}=I\alpha$

$\Rightarrow m_{1}g\left(l/2\right)-m_{2}g\left(l/2\right)=\left[m_1\right(l/2{)}^2+m_2\left(l/2{)}^2\right]\alpha$

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

$\Rightarrow \alpha =2{\text{rad/s}}^2$

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