First slide

Stress and strain

Question

When a solid cylinder of radius R is subjected to an axial tensile force, the elongation produced in it is found to be x. When a hollow cylinder of inner radius R and outer radius y, made of same material and having same length is subjected to same tensile axial force, Then elongation produced in it is found to be x. Then the value of $\frac{y}{R}$ is

Easy

A

$\sqrt{3}$
B

$2 \sqrt{2}$
C

2
D

$\sqrt{2}$

Solution

$x = \frac{p . l}{({πR}^{2}) Y} = \frac{p . l}{π (y^{2} - R^{2}) Y} \Rightarrow y = \sqrt{2} R$

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