Q. The work done by a force $\overrightarrow{F} = \left( - 6x^{3}i \right)N$, in displacing a particle from $x = 4\ m$ to $x = - 2\ m$ is
A) $360\ J$
B) $240\ J$
C) $- 240\ J$
D) $- 360\ J$
Explanation
(a) $W = \int_{A}^{B}F_{x}\ dx\ \Rightarrow W = \int_{x = 4}^{k = - 2}\left( - 6x^{3} \right)dx$
$= - 6\left\lbrack \frac{x^{4}}{4} \right\rbrack_{x = 4}^{x = - 2} = \left( \frac{- 3}{2} \right)( - 240) = 360\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.