Question

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

• A. 23 J
• B. 68 J
• C. 84 J
• D. 8 J

Answer 1

Answer: (D)

Force applied $F=10N$
Stretching in the spring $x=1mm=0.001m$
$\therefore$ spring constant $k=\frac{F}{x}=\frac{10}{0.001}=10^4$
Now the spring is stratched through a distance
$x_1=40mm$
$=0.04m$
The force required to stretch it through $x_1$ is $F_1=k{x}_1$
$\therefore$ The work done by this force $W=\frac{1}{2}k{x}_1^2$
$=\frac{1}{2}\times 10^4\times 0.04\times 0.04$
$\frac{1}{2}\times 16=8J$