Question

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

• A. $84\text{J}$
• B. $68\text{J}$
• C. $24\text{J}$
• D. $8\text{J}$

Answer 1

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

We know that work done by the spring force is given by
$W_s=\frac{1}{2}k{x}^2$

$k=\frac{F}{x}=\frac{10}{.001}={10}^4\text{N/m}$

$W=\frac{1}{2}k{x}^2=\frac{1}{2}\times {10}^4\times {\left(\frac{40}{1000}\right)}^2$

$\frac{1}{2}\times {10}^4\times \frac{16}{{10}^4}=8\text{J}$

Hence option D is the correct answer