First slide

Physical quantities and units

Question

In C.G.S. system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, meter and minute, the magnitude of the force is

Moderate

A

0.036
B

0.36
C

3.6
D

36

Solution

$\begin{matrix} n_{2} = n_{1} {(\frac{M_{1}}{M_{2}})}^{1} {(\frac{L_{1}}{L_{2}})}^{1} {(\frac{T_{1}}{T_{2}})}^{- 2} \\ = 100 {(\frac{gm}{kg})}^{1} {(\frac{cm}{m})}^{1} {(\frac{\sec}{min})}^{- 2} \\ = 100 {(\frac{gm}{10^{3} gm})}^{1} {(\frac{cm}{10^{2} cm})}^{1} {(\frac{\sec}{60 \sec})}^{- 2} \\ \Rightarrow n_{2} = \frac{3600}{10^{3}} = 3.6 \end{matrix}$

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