Question

The value of universal gravitational Constant G = $6.67\times {{10}^{-11}}N{{m}^{2}}K{{g}^{-2}}$. The value of G in units of ${{g}^{-1}}c{{m}^{3}}{{s}^{-2}}$ is?

Answer 1

Hint:Convert the Newton unit into its SI base units and then convert the mass and distance dimensions in the CGS unit i.e. Kilogram to gram and meter to centimeter. SI represents the international systems of units, that is why SI units are considered as the standard to represent any system.

Complete Step by Step Solution:
The universal gravitational constant is introduced in Newton's law which relates the force between two masses separated by some distance. The value of universal gravitational constant is:
G = $6.67\times {{10}^{-11}}N{{m}^{2}}K{{g}^{-2}}$.
Where, \[N{{m}^{2}}K{{g}^{-2}}\] is its SI unit.

In the given problem, we are asked to convert the SI unit of G to the CGS units i.e. ${{g}^{-1}}c{{m}^{3}}{{s}^{-2}}$.

To do this conversion, first we need to know the SI base units of newton which is:
$mKg{{s}^{-2}}$.

The gravitational constant in terms of SI base units will be: $K{{g}^{-1}}{{m}^{3}}{{s}^{-2}}$.
Applying the basic conversion factors, i.e., 1 Kg = 1000g and 1 m = 100 cm.

Substituting these conversion factors will give us the following form of G:
$G=6.67\times {{10}^{-11}}\times \dfrac{{{10}^{6}}c{{m}^{3}}}{{{10}^{3}}g}{{s}^{-2}}$

Hence, the final value of gravitational constant in terms of ${{g}^{-1}}c{{m}^{3}}{{s}^{-2}}$ will be
$G=6.67\times {{10}^{-8}}{{g}^{-1}}c{{m}^{3}}{{s}^{-2}}$

Note:
SI represents the international systems of units, that is why SI units are considered as the standard to represent any system. Sometimes considerations of units also depend on the scale of the measurements, for small scaling systems one might use the CGS units. Though SI units are more comfortable in calculations. For the given problem, one can also take a different approach i.e., converting Newton into dynes, CGS unit of force, and then write the dyne in its base units.