Question
An atmospheric pressure is 106 dyne/cm². Find its value in SI unit system.
✓
Answer
Dimension formula of pressure $=\left[ M ^1 L^{-1} T^{-2}\right]$
Here $a=1, b=-1, c=-2$
From the system converting equation :
$
n_2=n_1\left[\frac{M_1}{M_2}\right]^{a}\left[\frac{L_1}{L_2}\right]^{b}\left[\frac{T_1}{T_2}\right]^{c}
$
It is given,
CGS System
$M _1=1 gm$
$L _1=1 cm$
$T _1=1 s$.
MKS System
$M _2=1 kg$
$L _2=1 m$
$T _2=1 s$
$n_1=10^6$ dyne $/ cm ^2 \quad n_2=?$
$\begin{aligned} n_2 & =10^6\left[\frac{1 g}{1 kg}\right]^1\left[\frac{1 cm}{1 m}\right]^{-1}\left[\frac{1 s}{1 s}\right]^{-2} \\ & =10^6\left[\frac{1 g}{10^3 g}\right]^1\left[\frac{1 cm}{10^2 cm}\right]^{-1}\left[\frac{1 s}{1 s}\right]^{-2} \\ & =10^6\left[\frac{1 g}{10^3 g}\right]^1\left[\frac{10^2 cm}{1 cm}\right]^1 \\ & =\frac{10^6 \times 10^2}{10^3}=10^5\end{aligned}$
Hence atmospheric pressure in SI units $=10^5 N / m ^2$.
Here $a=1, b=-1, c=-2$
From the system converting equation :
$
n_2=n_1\left[\frac{M_1}{M_2}\right]^{a}\left[\frac{L_1}{L_2}\right]^{b}\left[\frac{T_1}{T_2}\right]^{c}
$
It is given,
CGS System
$M _1=1 gm$
$L _1=1 cm$
$T _1=1 s$.
MKS System
$M _2=1 kg$
$L _2=1 m$
$T _2=1 s$
$n_1=10^6$ dyne $/ cm ^2 \quad n_2=?$
$\begin{aligned} n_2 & =10^6\left[\frac{1 g}{1 kg}\right]^1\left[\frac{1 cm}{1 m}\right]^{-1}\left[\frac{1 s}{1 s}\right]^{-2} \\ & =10^6\left[\frac{1 g}{10^3 g}\right]^1\left[\frac{1 cm}{10^2 cm}\right]^{-1}\left[\frac{1 s}{1 s}\right]^{-2} \\ & =10^6\left[\frac{1 g}{10^3 g}\right]^1\left[\frac{10^2 cm}{1 cm}\right]^1 \\ & =\frac{10^6 \times 10^2}{10^3}=10^5\end{aligned}$
Hence atmospheric pressure in SI units $=10^5 N / m ^2$.
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