Question

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 :

• A. $2 \sqrt{\frac{p}{k}}$
• B. $ \sqrt{\frac{2p}{k}}$
• C. $ \sqrt{\frac{2k}{p}}$
• D. $2 \sqrt{\frac{k}{p}}$

Answer 1

Answer: (A)

$\frac{dp}{dt} = F = kt $
$ \int^{3P}_{P} dP = \int^{T}_{O} kt dt $
$ 2p = \frac{KT^{2}}{2} $
$ T = 2 \sqrt{\frac{P}{K}} $