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

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

Answer 1

The correct option is B

$\frac{1}{2}C{x}_1^2$

$W\underset{0}{\overset{x_1}{\int }}F.dx=\underset{0}{\overset{x_1}{\int }}Cxdx=C[\frac{x^2}{2}{]}_0^{x_1}=\frac{1}{2}C{x}_1^2$