Question

A particle with linear momentum of magnitude $P$ is subjected to a force $F=Kt \, \left(K > 0\right)$ which is directed along the direction of initial momentum. The time after which its linear momentum changes to $3P$ is

• A. $\sqrt{\frac{2 P}{K}}$
• B. $2\sqrt{\frac{P}{K}}$
• C. $\sqrt{\frac{2 K}{P}} \, $
• D. $2\sqrt{\frac{K}{P}}$

Answer 1

Answer: (B)

$F=\frac{dp}{dt}\Rightarrow Kt=\frac{dp}{dt}$
$\displaystyle \int _{P}^{3 P}dP=\displaystyle \int _{0}^{t}Ktdt\Rightarrow 3P-P=\frac{Kt^{2}}{2}\Rightarrow t=2\sqrt{\frac{P}{K}}$