If the unit of force is 100N, unit of length is 10m and unit of t… - Vidyadip

Question

If the unit of force is 100N, unit of length is 10m and unit of time is 100s, what is the unit of mass in this system of units?

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Answer

Dimension of force $=[\text{M}^1\text{L}^1\text{T}^2]=100\text{N}\ ...(\text{i})$ Dimension of length $=[\text{L}^1]=10\text{m}\ ...(\text{ii})$ Dimension of time $=[\text{T}^1]=100\text{s}\ ...(\text{iii})$ Substituting (ii), (iii) in (i) $\text{M}\times(10)\times(100)^{-2}=100$ $\frac{10\text{M}}{100\times100}=100$ $\text{M}=10^5\text{Kg L}=10^1\text{m}$ $\text{F}=10^2\text{N}\ \ \text{T}=10^2\text{sec}$

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