Question

A hollow cylinder of inner radius of $3cm$ and outer radius $5cm$ and a solid cylinder of radius $2cm$ are subjected to the same force. If they are made of same material and have same length the ratio of their elongation is

• A. $1:1$
• B. $1:2$
• C. $1:4$
• D. $2:3$

Answer 1

The correct option is C $1:4$

$F=YA\frac{\Delta L}{L}$

Here , force is same , Y is same , L is same for both the cylinders, hence equation reduces to: $A_1\left(\Delta L_1\right)=A_2\left(\Delta L_2\right)$

$\begin{array}{c}\pi (25-9)\left(\Delta L_1\right)=\pi \left(4\right)\left(\Delta L_2\right)\\ \therefore \frac{\Delta L_1}{\Delta L_2}=\frac{1}{4}\end{array}$