Q. A force $F = Ay^{2} + By + C$ acts on a body in the $y$-direction. The work done by this force during a displacement from $y = - a$ to $y = a$ is
A) $\frac{2Aa^{3}}{3}$
B) $\frac{2Aa^{3}}{3} + 2Ca$
C) $\frac{2Aa^{3}}{3} + \frac{Ba^{2}}{2} + Ca$
D) None of these
Explanation
(b) $W = \int_{}^{}{Fdy}$
$= \int_{- a}^{+ a}{(Ay^{2} + By + C)dy}$
$= \left\lbrack \frac{Ay^{3}}{3} + \frac{By^{2}}{2} + Cy \right\rbrack_{- a}^{+ a}$
$= \left\lbrack \frac{Aa^{3}}{3} + \frac{Ba^{2}}{2} + Ca \right\rbrack - \left\lbrack - \frac{Aa^{3}}{3} + \frac{Ba^{2}}{2} - Ca \right\rbrack$
$= \frac{2Aa^{3}}{3} + 2Ca$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.