Question

Each wire in the shown figure has cross-section $5\times {10}^{-3}{\text{cm}}^2\text{and}Y=2\times {10}^{11}\text{Pa}.P,Q$ and $R$ have mass $3\text{kg}$ each. Find the strain developed in string $A$. Assume the surface to be smooth and the pulley and strings to be massless and frictionless.

• A. ${10}^{-5}$
• B. ${10}^{-3}$
• C. ${10}^{-4}$
• D. None

Answer 1

The correct option is C ${10}^{-4}$


Let acceleration of each mass be $a$
Using Newtons second law, we get
$3g-T_1=3a-\left(1\right)$
$T_1-T_2=3a-\left(2\right)$
$T_2=3a-\left(3\right)$
Adding (1), (2) and (3)
$a=\frac{g}{3};T_2=3a=g$
Strain in $A$ is
$\frac{\Delta l}{l}=\frac{F/A}{Y}=\frac{T_2}{AY}=\frac{g}{5\times {10}^{-3}\times 2\times {10}^{11}\times {10}^{-4}}={10}^{-4}$