Question

A uniform rod of length $l$ and mass $M$ is suspended from two inextensible string as shown in the figure. What will be the tension in the left string when right string snaps?

• A. $\frac{m g}{2}$
• B. $mg$
• C. $\frac{m g}{4}$
• D. $\frac{m g}{8}$

Answer 1

Answer: (C)

Using Newton's second law on rod,
$mg-T=ma...\left(i\right)$

Using the torque equation about the left string,
$\frac{m g l}{2}=I\alpha =\frac{m l^{2}}{3}\times \frac{a}{\left(l/2\right)}$
$\Rightarrow a=\frac{3 g}{4}$ .
Putting the value of $a$ in equation $\left(i\right)$ ,
$T=\frac{m g}{4}$ .