Question

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

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

Answer 1

Answer: (D)

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