Shown in the figure is a rigid and uniform one-meter-long rod $ AB$ held in a 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 $ 2 m$ hung at a distance of $ 75 cm$ from $ A$. The tension in the string at $ A$ is:

o 25 50 75 100 B

$0.75 m g$

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$0.5 m g$

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$1 m g$

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$2 m g$

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Solution

The correct option is C
$1 m g$

Explanation for the correct answer:
Finding the tension in the string $A$ :
At equilibrium torque about any axis must be zero. Taking the torque about $B$ .
$\Rightarrow T \times 100 c m = m g \times 50 c m + 2 m g \times 25 c m \Rightarrow 100 T = 50 + 50 \Rightarrow 100 T = 100 \Rightarrow T = \frac{100}{100} \Rightarrow T = 1 m g$
Therefore, the correct answer is option (C).

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