Question

The linear momentum $p$ of a body moving in one dimension varies with time $t$ according to the equation $p = a + bt^2$, where $a$ and $b$ are positive constant. The net force acting on the body is

• A. a constant
• B. proportional to $t^2$
• C. inversely proportional to $t$
• D. proportional to $t$

Answer 1

Answer: (D)

proportional to $t$

Answer 2

Given, $P = a + bt^2$ $\frac{dP}{dt} = 2bt$ $\because F = \frac{dP}{dt}$ $\therefore F = 2bt$ or $F \propto t$