Q.
The linear momentum $\rho$ of a body moving in one dimension varies with time according to the equation $\rho = a + bt^{2}$ where $a$ and $b$ are positive constants. The net force acting on the body is
A) A constant
B) Proportional to $t^{2}$
C) Inversely proportional to $t$
D) Proportional to $t$
Explanation
(d) $F = \frac{dp}{dt} = \frac{d}{dt}\left( a + bt^{2} \right) = 2bt\ \therefore F \propto t$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.