Question

Differentiate between 'g' and 'G'. also derive relation between them

Answer 1

Dear Student

Universal gravitation constant(G)
1.It is define as the force of attraction acting between two bodies each of unit mass, whose centers are placed unit distance apart.
2. Its value is same throughout the universe .
3. It is a scalar quantity .
4. Its value dose not depends upon the nature and the size of the bodies.

5. Dimensional formula for G is [M^-1L³T^-2].

Acceleration due to gravity(g)

1.It is define as the constant acceleration produced in a body when it falls freely under the effect of gravity .

2. its value changes from place to place.

3. it is a vector quantity.

4. Its value depends upon the nature and the size of the bodies.

5. Dimensional formula for g is [M⁰L¹T^-2].

Rel20is
$$\begin{gathered} F_g=F_G \\ mg=\frac{Gm{M}_{planet}}{{r_{planet}}^2} \\ g=\frac{G{M}_{planet}}{{r_{planet}}^2} \end{gathered}$$