IIT JEE , AIEEE Forum - Physics , General

rooney

Momentum is conserved in any frame.
So, mdy/dt = m₀dy/d

(Assuming that relative vel of frame is only along x-axis. So conserving momentum along y-axis)
LHS is as observed by observer in his frame of reference of rest S.
RHS is as observed by another observer in frame of reference S' of object which is moving with relative vel. v with respect to the S.
m=m₀d

/dt

Now d

is the time period measured by observer in frame of reference S' of object.
dt " " " " " " " " " " " S.

There is something called time dilation. Means that when you measure the time period of event taking place in another frame of reference moving with vel. v , the time you measure is more than the actualy time period by a factor of (1 - v²/c²)^1/2.Hence,
d

/dt = 1/(1 - v²/c²)^1/2.

Put this in earlier equation ,
m = m₀/(1 - v²/c²)^1/2.

Hope it helps.

-Rohil

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