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

Answer: (B)

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