Question

When a tension 'F' is applied , the elongation produced in uniform ire of length l ,radius r is e , when tension 2F is applied , the elongation produced in another uniform wire of length 2l and radius 2r made of same material is :

• A. 0.5 e
• B. 1.0 e
• C. 1.5 e
• D. 2.0 e

Answer 1

Answer: (B)

1.0 e

Lets consider $x$ be the elongation produce in wire when $2F$ is applied of radius $2r$ and length $2l.$

The material of wire is same, so young's modulus is equal.

$Y=Y^{\prime }$

$\frac{F/A}{e/l}=\frac{2F/A^{\prime }}{x/2l}$

$\frac{1}{Ae}=\frac{4}{A^{\prime }x}$

$\frac{1}{\pi r^2.e}=\frac{4}{4\pi r^2.x}$

$\frac{1}{e}=\frac{1}{x}$

$x=1.0e$

The correct option is B.