Question

Find out work done by applied force to slowly extend the spring from x to 2x.

• A. $\frac{1}{2}k{x}^2$
• B. $\frac{3}{2}k{x}^2$
• C. $\frac{5}{2}k{x}^2$
• D. $\frac{7}{2}k{x}^2$

Answer 1

The correct option is B $\frac{3}{2}k{x}^2$

Initially the spring is extended by x
$W=\overrightarrow{F}.\overrightarrow{ds}$
$W={\int }_k^{2x}Kx.dx$
$W={\left[\frac{K{x}^2}{2}\right]}_x^{2x}=\frac{3}{2}K{x}^2$
It can also found by difference of PE.
i.e.
$U_f=\frac{1}{2}K(2x{)}^2=2K{x}^2\Rightarrow U_i=\frac{1}{2}K{x}^2\Rightarrow U_f-U_i=\frac{3}{2}K{x}^2$