Q 11-04-191JEE MainJEE Main 2019 (11 Jan, Shift 2)Easy
A particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t = 0$, a force $F = kt$ acts in the same direction on the moving particle during time interval $T$ so that its momentum changes from $p$ to $3p$. Here $k$ is a constant. The value of $T$ is
Answer: (B) $2\sqrt{\dfrac pk}$
Impulse equals the change in momentum:
$$\int_0^T kt\,dt = \frac{kT^2}{2} = 3p - p = 2p \Rightarrow T = 2\sqrt{\frac pk}$$
Solution by Sreeraj P, M.Sc Physics