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A particle of mass is moving in a stra...

A particle of mass 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 constant . The value of T is :

A

`sqrt((2p)/(k))`

B

`2 sqrt((k)/(p))`

C

`sqrt((2k)/(p ))`

D

`2 sqrt((p)/(k))`

Text Solution

Verified by Experts

The correct Answer is:
D
`(dvecP )/(dt ) =vecF," " d vecP =vecF dt, " "Delta vecP=int vecFdt`
`therefore 2P-P= int _(0) ^(T) ktdt`
`2P = (KT^(2))/(2)," "T=2 sqrt((P)/(K)).`
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