A spring 40 mm long is streched by application of a force. If 10 N force is required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is

Question

\[(a)\;84\;J \quad (b)\;68 \;J\quad (c)\; 23\;J \quad (d)\;8\;J\]

Answer 1

Since 10 N force is required to stretch through 1 mm

$k=\large\frac{Force}{extension}$

$\quad=\large\frac{10}{10^{-3}}$

$k=10^4\;N/m$

$E=\large\frac{1}{2}$$kx^2$

$\quad=\large\frac{1}{2} $$\times 10^4 \times (40 \times 10^{-3})^2$

$\quad = 8\;J$

Hence d is the correct answer.