Question

Prove the force = mass x acceleration. State the condition when it holds.

Answer 1

The rate of change of momentum = `(Δp)/(Δt) = (Δ(mv))/(Δt)`

(When v → c or m is not constant)

But if mass m is constant i.e v < c.

rate of change of momentum = `(Δp)/(Δt) = m (Δv)/(Δt)`

Here the quantity `(Δv)/(Δt)` = rate of change of velocity i.e., acceleration a.

The rate of change in momentum = `(Δp)/(Δt) = m (Δv)/(Δt) = ma`

Thus by Newton's second law of motion or F = k ma.

where k is a constant of proportionality which can be made equal to 1 by choosing the suitable unit for force.

Hence, F= ma when mass m of the body is constant at velocity v which is much smaller than the velocity of light.