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. $c{x}_1^3$
• D. zero

Answer 1

Answer: (B)

$F=cx$
$W=\int F.dx$
$W={\int }_0^{x_1}cx.dx$
$F={\left[c\frac{x^2}{2}\right]}_0^{x_1}$
$F=c\frac{x_1^2}{2}$