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 :

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 √(p/k) (B)  √(2p/k) (C)  √(2k/p) (D) 2 √(k/p)

Tardigrade Admin · Accepted Answer

(dp/dt) = F = kt ∫3PP dP = ∫TO kt dt 2p = (KT2/2) T = 2 √(P/K)

Q. A particle of mass $m$ is moving in a straight line with momentum $p$ . Starting at time $t = 0$ , a force $F = k t$ acts in the same direction on the moving particle during time interval $T$ so that its momentum changes from $p$ to $3 p$ . Here $k$ is a constant. The value of $T$ is :

$2 \frac{p}{k}$

$\frac{2 p}{k}$

$\frac{2 k}{p}$

$2 \frac{k}{p}$

$\frac{d p}{d t} = F = k t$
$\int_{P}^{3 P} d P = \int_{O}^{T} k t d t$
$2 p = \frac{K T ^{2}}{2}$
$T = 2 \frac{P}{K}$

Q. 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 :

2kp​​

k2p​​

p2k​​

2pk​​