Question

A light rod of length $1m$ is pivoted at its centre and two masses of $5kg$ and $2kg$ are hung from the ends as shown in figure. Find the initial angular acceleration of the rod assuming that it was horizontal in beginning.

• A. $8.4rad/s^2$
• B. $2rad/s^2$
• C. $1rad/s^2$
• D. $5rad/s^2$

Answer 1

The correct option is A $8.4rad/s^2$

$\tau =r\times F=I\alpha$

$5$ Kg block rotates clockwise whereas $2kg$ will rotate anticlockwise

So,

$\frac{1}{2}\times 5g-\frac{1}{2}\times 2g=I\alpha$

$\frac{3}{2}g=I\alpha$

$I=m{R}^2=5{\left(\frac{1}{2}\right)}^2\times 2{\left(\frac{1}{2}\right)}^2$

$I=\frac{7}{4}$

$\therefore \frac{3}{2}\times 9.8=\frac{7}{4}\alpha$

$\Rightarrow \alpha =8.4rad/s^2$