Q. The potential energy of a particle of mass 5 kg moving in the $x - y$ plane is given by $U = ( - 7x + 24y)$ J, $x$ and $y$ being in metre. Initially at $t = 0$ the particle is at the origin (0, 0) moving with a velocity of $(2.4\widehat{\mathbf{i}} + 0.7\widehat{\mathbf{j}})ms\ ^{- 1}$. The magnitude of force on the particle is
A) 25 units
B) 24 units
C) 7 units
D) None of these
Explanation
(a) $\overrightarrow{\mathbf{F}} = \frac{\partial U}{\partial x}\widehat{\mathbf{i}} - \frac{\partial U}{\partial y}\widehat{\mathbf{j}} = 7\widehat{\mathbf{i}} - 24\widehat{\mathbf{j}}$
$\left| \overrightarrow{\mathbf{F}} \right| = \sqrt{(7)^{2} + ( - 24)^{2}} = 25\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.