Question

A spring 40 mm long spring is stretched by applying a force. If 10 N force is required to stretch the spring through one mm, then work done in stretching the spring through 40 mm is :

• A. 24 J
• B. 8 J
• C. 56 J
• D. 64 J

Answer 1

The correct option is B 8 J

$\text{Step 1: Spring constant of spring}$

$F=10N$ is required to stretch the spring by $1mm$

From, $F=kx$

$\Rightarrow k=\frac{F}{x}=\frac{10N}{{10}^{-3}m}={10}^{4}N/m$

$\text{Step 2: Work done in stretching spring}$

Work done in stretching spring$=\frac{1}{2}k(x_f^2-x_i^2)$

Initially spring is at natural length i.e. $x_i=0$

Therefore, Work done in stretching through $40mm$, $W=\frac{1}{2}\times k\times (x_f{)}^2$

$\Rightarrow W=\frac{1}{2}\times {10}^4\times (40\times {10}^{-3}m{)}^2$

$\Rightarrow W=8J$

Hence, Option B is correct.