Question

A particle moves under the effect of a force $F=Cx$ from $x=0$ to $x=x_1$. The work done in the process is (treat $C$ as a constant):

• A. $\frac{C^2}{x_1^2}$
• B. $C{x}_1^2$
• C. $\frac{C{x}_1^2}{2}$
• D. $\frac{C}{x_1^2}$

Answer 1

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

Work Done $={\int }_0^{x_1}\overrightarrow{F}.d\overrightarrow{x}$ $={\int }_0^{x_1}Cx.dx$ $=\frac{C{x}_1^2}{2}$