Question

A particle moves along the $x$-axis from $x=x_{1}$ to $x=x_{2}$ under the action of a force given by $F=2 x$. Then the work done in the process is

• A. zero
• B. $x_{2}^{2}-x_{1}^{2}$
• C. $2 x_{2}\left(x_{2}-x_{1}\right)$
• D. $2 x_{1}\left(x_{1}-x_{2}\right)$

Answer 1

Answer: (B)

Mechanical work $(W)$ is the force applied through a distance, defined mathematically as the line integral of a scalar product of force $(F)$ and displacement $(d x)$ vectors
$W=\int F d x$
Given $F=2 x$
hence $W=\int\limits_{x_{1}}^{x_{2}} 2 x d x$
$=2\left[\frac{x^{2}}{2}\right]_{x_{1}}^{x_{2}}$ $=x_{2}^{2}-x_{1}^{2}$