Q. A body of mass 3 kg is under a force which causes a displacement in it, given by $s = t^{2}/3$ (in m). Find the work done by the force in 2 s
A) 2 J
B) 3.8 J
C) 5.2 J
D) 2.6 J
Explanation
(d) $W = \int_{0}^{2}{F\ ds = \int_{0}^{2}{Ma\ ds = \ \int_{0}^{2}{\ M\frac{d^{2}s}{dt^{2}}ds}}}$
$= \int_{0}^{2}{\ M\frac{d^{2}s}{dt^{2}}.\frac{ds}{dt}dt}$
$= \int_{0}^{2}{3\left( \frac{2}{3} \right)}.\left( \frac{2}{3}t \right)dt$
$= \frac{4}{3}\left\lbrack \frac{t^{2}}{2} \right\rbrack_{0}^{2}$
$W = \frac{4}{3} \times \frac{4}{2} = \frac{8}{3} = 2.6\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.