JEE Main201911 Jan 2019Evening ShiftPhysicsLaws of MotionActual
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
Options
- A2 k p
- B2 p k
- C2 k p
- D2 p k
Correct answer
B. 2 p k
Step-by-step solution
From Newton's second law dp dt = F = kt Integrating both sides we get, _ p ^ 3 p dp = ₀^ T ktdt [ p ]_ p ^ 3 p = k [ t ² 2 ]₀^ T 2 p = kT ² 2 T =2 p k