Question

A spring $40\text{mm}$ long is stretched by applying a force. If $10\text{N}$ force is required to stretch the spring through $1\text{mm}$, then work done in stretching the spring through $40\text{mm}$ is

• A. $24\text{J}$
• B. $8\text{J}$
• C. $56\text{J}$
• D. $64\text{J}$

Answer 1

The correct option is B $8\text{J}$

Force constant,
$k=\frac{F}{x}=\frac{10}{0.001}=10000\text{N/m}={10}^4\text{N/m}$

Work done $=\frac{1}{2}k{x}^2=\frac{1}{2}\times {10}^4\times {\left(\frac{40}{1000}\right)}^2$
$=\frac{1}{2}\times {10}^4\times \frac{16}{{10}^4}=8\text{J}$