A body of mass m moving with a velocity v is acted upon by a force. Write expression for change in momentum in each of the following cases (i) when v << c (ii) when v → c, and (iii) when v << c but m does not remain constant. Here c is the speed of light.

(i) When v << c

i.e., if the velocity of the moving particle is much smaller than the velocity of light (c), then —

Change in momentum (Δp) = m Δv

It happens when the velocity of the particle is of the order of 10⁶ m s^-1 or less than this, then the variation in mass with velocity is small enough and mass can be considered to be constant.

(ii) when v → c

Change in momentum (Δp) = Δ(mv)

(iii) when v << c but m does not remain constant.