Question

A person went to a petrol pump to get petrol and air filled in his car. The recommended tyre pressure in CGS units is $8\times {10}^6$ but the pressure gauges (instrument for pressure measurement) was calibrated in SI units. If the tyre was filled will right pressure, the reading of the pressure gauge is $k\times {10}^{5}units$. Find $k$.

Answer 1

Given, magnitude of force in C.G.S. system $=8\times {10}^6$

Let magnitude of pressure in SI system be $n_2$

$n_2=n_1{\left[\frac{M_1}{M_2}\right]}^1{\left[\frac{L_1}{L_2}\right]}^{-1}{\left[\frac{T_1}{T_2}\right]}^{-2}$

$n_2=8\times {10}^6{\left(\frac{gm}{kg}\right)}^1{\left(\frac{cm}{m}\right)}^{-1}{\left(\frac{sec}{sec}\right)}^{-2}$

$n_2=8\times {10}^6{\left(\frac{gm}{{10}^{3}gm}\right)}^1{\left(\frac{cm}{{10}^{2}cm}\right)}^{-1}{\left(\frac{sec}{sec}\right)}^{-2}$

$n_2=\frac{8\times {10}^6}{10}=8\times {10}^5=k\times {10}^{5}units$

$\therefore k=8$

Final answer : $8$