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For a relation F = m(Δv)Δt\dfrac{m(Δv)}{Δt}, to hold true, the condition(s) necessary is/are:

  1. velocities are equal to the velocity of light
  2. velocities are much smaller than the velocity of light
  3. mass remains constant
  4. both (b) and (c)

Laws of Motion

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Answer

both (b) and (c)

Reason — It is observed that the mass of a particle increases with increase in velocity but it becomes perceptible only when the velocity v of the particle is comparable with the speed of light c. At velocities v << c, the change in mass is not perceptible. At such velocities (v << c ), mass m can be considered to be constant. Then Newton's second law takes the form F = m(Δv)Δt\dfrac{m(Δv)}{Δt} = ma.

Thus, for F = m(Δv)Δt\dfrac{m(Δv)}{Δt} = ma to hold true, two conditions are required :

  1. velocities are much smaller than the velocity of light
  2. mass remains constant.

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