Question

A rod $\text{PQ}$ of mass of mass $M$ and length $L$ is hinged at end $\text{P}.$ The rod is kept horizontal by a massless string tied to point $\text{Q}$ as shown in figure. When string is cut, the initial angular acceleration of the rod is-

• A. $\frac{2g}{3L}$
• B. $\frac{3g}{2L}$
• C. $\frac{g}{L}$
• D. $\frac{2g}{L}$

Answer 1

The correct option is B $\frac{3g}{2L}$

When the string is cut,

$\tau =\overrightarrow{r}\times \overrightarrow{F}$

Also, $\tau =I\alpha$

For the rod $I=\frac{M{L}^2}{3}$

$\Rightarrow Mg\left(\frac{L}{2}\right)=\left(\frac{M{L}^2}{3}\right)\alpha$

$\Rightarrow \alpha =\frac{3g}{2L}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.