First slide

Physical quantities and units

Question

In a new system of units a tower of height 76 m is represented by number 7.6, sugar sack of mass 100 kg is represented by number 10 and 1 hour time is represented by number 360. If a force is measured to be 4 N then the magnitude of force in this new system is____________ units.

Moderate

Solution

Let new units of length, mass and time be L, M and T then 7.6 L=76 m
$\begin{array}{l} \Rightarrow L = 10 m \\ 10 M = 100 kg \\ M = 10 kg \\ 360 T = 3600 s \end{array}$
$\Rightarrow T = 10 s$
$4 N = n F$ where F is unit of force in new system.
$\Rightarrow n = \frac{4 kgm / s^{2}}{10 kg 10 m (10 s)^{- 2}} = 4$
$n_{1} u_{1} = n_{2} u_{2} 4 M_{1} L_{1} \frac{1}{{T^{2}}_{1}} = n M_{2} L_{2} \frac{1}{{T^{2}}_{2}} 4 M_{1} L_{1} \frac{1}{{T^{2}}_{1}} = n \frac{M_{1}}{10} \frac{L_{1}}{10} \frac{100}{{T^{2}}_{1}} ∴ n = 4$

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