Question

A particle moves along the $x$-axis from $x=x_1$ to $x=x_2$ under the action of a force given by $F=2x$. Then the work done in the process is

• A. zero
• B. $x_2^2-x_1^2$
• C. $2x_2\left(x_2-x_1\right)$
• D. $2x_1\left(x_1-x_2\right)$

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 $(dx)$ vectors
$W=\int Fdx$
Given $F=2x$
hence $W=\underset{x_1}{\overset{x_2}{\int }}2xdx$
$=2{\left[\frac{x^2}{2}\right]}_{x_1}^{x_2}$ $=x_2^2-x_1^2$