Question

A particle moves under the effect of a force $F=Cx$ form $x=0$ to $x=x_1$. The work done in the process is-

• A. $C{x}_1^2$
• B. $\frac{1}{2}C{x}_1^2$
• C. $C{x}_3^2$
• D. zero

Answer 1

The correct option is B $\frac{1}{2}C{x}_1^2$

Similar to a spring with neutral point at x=0

$W=\int \overline{F}.\overline{d}s={\int }_0^{x_1}Cxdx=0.5C{x}_1^2$