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  • Confused! kindly explain, 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

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 :

  • Option 1)

    2\sqrt{\frac{p}{k}}

  • Option 2)

    \sqrt{\frac{2p}{k}}

  • Option 3)

    2\sqrt{\frac{k}{p}}

  • Option 4)

    \sqrt{\frac{2k}{p}}

Answers (1)

best_answer

 

Newton's 2nd Law -

F\propto \frac{dp}{dt}

F=\tfrac{kdp}{dt} 

F=\tfrac{d\left (mv \right )}{dt} 

F=\tfrac{m\left (dv \right )}{dt}

\frac{dv}{dt}=a

Therefore  F=ma

- wherein

K=1 in C.G.S & S.I

Force can be defined as rate of change of momentum.

 

we know that

\frac{dp}{dt}=F

& F=kt

So, \frac{dp}{dt}=kt

\int_{p}^{3p}dp=\int_{o}^{T}kt dt

2p=\left [ \frac{kt^{2}}{2} \right ]_{0}^{T}=\frac{kT_{2}}{2}

T=2\sqrt{\frac{P}{K}}

 

 


Option 1)

2\sqrt{\frac{p}{k}}

Option 2)

\sqrt{\frac{2p}{k}}

Option 3)

2\sqrt{\frac{k}{p}}

Option 4)

\sqrt{\frac{2k}{p}}

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