Question

The value of Gravitational constant is \[G = 6.67 \times {10^{ - 11}}N - {m^2}/k{g^2}\] SI units. Convert it into a CGS system of units.
$
  {\text{A}}{\text{. Thus, the value of G in CGS}}{\text{ system of units is 6}}{\text{.67}} \times {\text{1}}{{\text{0}}^{ - 8}}{\text{ dyne c}}{{\text{m}}^2}/{g^2}. \\
  {\text{B}}{\text{. Thus, the value of G in CGS}}{\text{ system of units is 6}}{\text{.67}} \times {\text{1}}{{\text{0}}^{ - 9}}{\text{ dyne c}}{{\text{m}}^2}/{g^2}. \\
  {\text{C}}{\text{. Thus, the value of G in CGS}}{\text{ system of units is 6}}{\text{.67}} \times {\text{1}}{{\text{0}}^{ - 7}}{\text{ dyne c}}{{\text{m}}^2}/{g^2}. \\
  {\text{D}}{\text{. Thus, the value of G in CGS}}{\text{ system of units is 6}}{\text{.67}} \times {\text{1}}{{\text{0}}^{ - 10}}{\text{ dyne c}}{{\text{m}}^2}/{g^2}. \\
$

Answer 1

Hint: SI system is in Newton, meters, and kilograms. The CGS system has dynes, centimeters, and grams. Using the relation between Newton and dynes, meters and centimeters, kilograms and grams convert the SI units into CGS.

Complete step-by-step solution -
Any object having mass has the property to attract other objects. This force of attraction that arises because of the mass of an object is called the gravitational force. Gravitational force is an attractive force and it never pushes things away.
The force of gravity is directly proportional to the product of the masses of the object and is inversely proportional to the square of the distance between them.
${F_G} = \dfrac{{G \times {m_1} \times {m_2}}}{{{r^2}}}$
Where, G is called the universal gravitational constant and has a value $6.67 \times {10^{ - 11}}N - {m^2}/k{g^2}$. This force follows the action-reaction law of Newton. This means that force exerted by object 1 on object 2 is the same as the force exerted by object 2 on object 1. For instance, the earth exerts the same force on you as you exert on earth.
It is the weakest fundamental force of nature. As it is an inverse square law, the force of gravity never becomes 0 even at infinite distance.
We are surrounded by gravitational force. It is the force of gravity that determines the weight of an object. This force reduces as we go above the surface of the earth. As the mass of the Moon is less than that of the earth one will feel less force on the Moon. This is why astronauts feel like flying in outer space and on the Moon.
Converting the units:
$1N = {10^5}dynes$ ; 1m =100 cm ; 1kg = 1000 g
$ G = 6.67 \times {10^{ - 11}} \dfrac{N \times {m^2}}{{kg}^2} \\ $
$ G = \dfrac{{6.67 \times {10^{-11}}} \times (10^5) dynes \times (100 \times 100) cm^2}{(1000 \times 1000) g^2}$
$ G = 6.67 \times {10^{-8}} dynes \times cm^2/g^2$

The correct option is (A).

Note: It is important to know the relation between certain units to do these types of questions, and a proper substitution should be made to get the answer.