Q. A particle moves along the x$- a$xis 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) $2x_{2}(x_{2} - x_{1})$
D) $2x_{1}(x_{1} - x_{2})$
Explanation
(d) Given $F = 2x$,
Work done $W = \int_{}^{}{F\ dx}$
$\therefore W = {\int_{x_{1}}^{x_{2}}{2x\ dx = 2\left\lbrack \frac{x^{2}}{2}\ \right\rbrack}}_{x1}^{x2}$
=$(x_{2}^{2} - x_{1}^{2})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.