Question

How to show that kgm/s and N.s represent the same quantity ? Also what is that quantity

Answer 1

N.s=Kgm/s^2 ×s =Kgm/s.

The quantity is momentum.

Answer 2

Given: 2 units

To Prove: kgm/s = N.s and represent the same quantity.

quantity =?

Solution:

N - Newton is the SI unit used for force.

Formulas:-

The Formula for force = mass(m) × acceleration(a)

The formula for acceleration = velocity(v) × time(t)

The formula for velocity = displacement (s)/time(t)

∴ acceleration (a) = s/t²

S.I unit for the quantities are as follows:-

mass - m = kilogram - kg

Distance/Displacement- s = meter - m

time - t = seconds - s

Force - F = Newton - N

Hence Force = m × s/t²

               F = $\frac{m . s}{t^{2} }$

               F = kg × m/s²

  1 Newton = 1 kgms⁻²

Multiplying time on both sides:-

1 N.s = 1 $\frac{kg.m.s}{s^{2} }$

1 N.s = 1 kgms⁻¹

Hence proved.

The Quantity that the above units represent is momentum "p".

p = mv (m - mass, v - velocity) or F × t

unit = kgm/s