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

Question

A particle with linear momentum of magnitude P is subjected to a force F=Kt (K > 0) which is directed along the direction of initial momentum. The time after which its linear momentum changes to 3P is (A) √(2 P/K) (B) 2√(P/K) (C) √(2 K/P)  (D) 2√(K/P)

Tardigrade Admin · Accepted Answer

F=(dp/dt)⇒ Kt=(dp/dt) displaystyle ∫ P3 PdP= displaystyle ∫ 0tKtdt⇒ 3P-P=(Kt2/2)⇒ t=2√(P/K)

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

$\frac{2 P}{K}$

$2 \frac{P}{K}$

$\frac{2 K}{P}$

$2 \frac{K}{P}$

$F = \frac{d p}{d t} \Rightarrow K t = \frac{d p}{d t}$
$\int_{P}^{3 P} d P = \int_{0}^{t} K t d t \Rightarrow 3 P - P = \frac{K t ^{2}}{2} \Rightarrow t = 2 \frac{P}{K}$

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

K2P​​

2KP​​

P2K​​

2PK​​