A spring of $5 \times 10^3 \mathrm{Nm}^{-1}$ spring constant is stretched initially by 10 cm from…
A spring of $5 \times 10^3 \mathrm{Nm}^{-1}$ spring constant is stretched initially by 10 cm from unstretched position. The work required to stretch it further by another 10 cm is
$75 \mathrm{~N}-\mathrm{m}$
$50 \mathrm{~N}-\mathrm{m}$
$76 \mathrm{~N}-\mathrm{m}$
$82 \mathrm{~N}-\mathrm{m}$
Solution
The work done required to stretch a spring from $\mathrm{x}_1$ to $x_2$ is
$\mathrm{W}=\frac{1}{2} \mathrm{k}\left(\mathrm{x}_2^2-\mathrm{x}_1^2\right)$
$=\frac{1}{2} \times 5 \times 10^3\left[\left(20 \times 10^{-2}\right)^2-\left(10 \times 10^{-2}\right)^2\right]=75 \mathrm{~N}-\mathrm{m}$