Question

Shown in the figure is a rigid and uniform one meter long rod $AB$ held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass $m$ and has another weight of mass $2m$ hung at a distance of $75\text{cm}$ from $A$. The tension in the string at $A$ is :

• A. $0.5mg$
• B. $2mg$
• C. $0.75mg$
• D. $1mg$

Answer 1

The correct option is D $1mg$

Net torque, ${\tau }_{net}$ about $B$ is zero at equilibrium,


$\Rightarrow (T_A\times 100)-(mg\times 50)-(2mg\times 25)=0$

$\Rightarrow T_A\times 100=100mg$

Therefore, Tension in the string at $A$

$T_A=1mg$

Hence, option $\left(D\right)$ is correct.