Question

Under the action of a force $F=Cx$, the position of a body changes from $0$ to $x$. The work done is :

• A. $\frac{1}{2}C{x}^2$
• B. $C{x}^2$
• C. $Cx$
• D. $\frac{1}{2}Cx$

Answer 1

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

Work done $W={\int }_0^{x}Fdx$

$W={\int }_0^{x}Cxdx$

$W=C\times \frac{x^2}{2}{|}_0^x$

$\therefore$ $W=\frac{C}{2}\times (x^2-0)$ $⟹W=\frac{1}{2}C{x}^2$