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Question

A particle of mass m is moving in a straight line with momentum p. Starting at time t=0, a force F=kt (k is a constant) acts along the direction of motion of particle for the time interval T so that its momentum changes from p to 5p. The value of T is

A
2pk
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B
2pk
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C
22pk
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D
2kp
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Solution

The correct option is C 22pk
From newton's 2nd law of motion :
F=dpdt ...(i)
F=kt, Pi=p, Pf=5p
And ti=0, tf=T
Integrating Eq. (i) on both sides with suitable limits :
t=Tt=0Fdt=5ppdp
t=Tt=0kt dt=5ppdp
[kt22]T0=[p]5pp
kT22=[5pp]=4p
T=8pk=22pk

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