Question

The ratio of the value of G in SI units to CGS units is

• A. ${10}^3:1$
• B. ${10}^2:1$
• C. ${10}^{-2}:1$
• D. ${10}^{-3}:1$

Answer 1

The correct option is A ${10}^3:1$

$\text{Quantity}$	$\text{SI System}$	$\text{CGS System}$
Force	Newton (N)	dyne
Distance	metre (m)	centi-meter (cm)
Mass	kilogram (kg)	gram (g)

The unit of G can be calculated by putting the unit of all the quantities in the expression of the force due to gravity.

$\frac{G{m}_1{m}_2}{r^2}=F$ $\Rightarrow G=\frac{F\times r^2}{m_1\times m_2}$

So we get, $\text{Unit of G}=\frac{\text{Unit of force}\times {\text{(Unit of distance)}}^2}{{\text{(Unit of mass)}}^2}$

$\text{SI unit of G}=\frac{N.m^2}{k{g}^2}$ and $\text{CGS unit of G}=\frac{dyne.c{m}^2}{g^2}$

We know that $1N={10}^{5}dyne$, $1kg={10}^{3}g$ and $1m={10}^{2}cm$

$\underset{–}{\text{Required ratio:}}$

$\frac{SI}{CGS}=\frac{N.m^2.g^{-2}}{dyne.c{m}^2.k{g}^{-2}}=\frac{{10}^{5}dyne\times {10}^{4}c{m}^2\times g^{-2}}{dyne\times c{m}^2\times {10}^{-6}{g}^{-2}}={10}^3:1$

So the answer is option A.