Question

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

Answer 1

According to the questions,

$m_1=200g,l=1m,m_2=20g$

Therefore,

$(T_1\times r_1)-(T_2\times r_2)-(m_{1}g\times r_3)=0$

$\Rightarrow T_1\times 0.7-T_2\times 0.3-2\times 0.2\times g=0$

$\Rightarrow 7T_1-3T_2=3.92...\left(1\right)$

$T_1+T_2=2\times 9.8+0.02\times 9.8$

= 1.96 + 0.196 = 2.156

$=1.96+0.196=2.156$ Adding (1) and (2), we get,

$3T_1+3T_2=6.468...\left(2\right)$

$\text{Adding}\left(1\right)\text{and}\left(2\right),\text{we get,}$

$10T_1=10.3$

$\Rightarrow T_1=1.038N=1.04N$

Therefore,

$\text{Therefore,}{T}_2=2.156-1.038$

$=1.18\simeq 1.12\text{N}$