Question

A uniform metre stick of mass $200g$ is suspended from the ceiling through two vertical strings of equal lengths fixed t the ends. A small object of the mass $20g$ is placed on the stick at the distance of $70cm$ from the left end. Find the tension in two strings.

Answer 1

Mass of stick (M) $=0.2kg$

Mass of object(m) $=0.02kg$

The weight of the stick is $0.2\times 10=2N$

The weight of the small object is $0.02\times 10=0.2N$

As the system is in equilibrium,

$T_1+T_2=2+0.2=2.2N$..............(1)

Stick does't rotate, so net torque is zero,

Torque about mid point,

$(0.2\times 0.2)+(T_1\times 0.5)=(T_2\times 0.5)$

$\Rightarrow (T_2-T_1)0.5=0.04$

$T_2-T_1=0.08$..............(ii)

From eq (i) and (ii)

$2T_2=2.28N$

$T_2=1.14N$

$T_1=(1.14-0.08)N$

$=1.06N$