Question

derive an expression for acceleration due to gravity of earth or obtain the relation betn the universal gravitation and the gravitational acceleration​

Answer 1

g=GM/r^2is that relation among them

Answer 2

Acceleration due to gravity of Earth is given as  g =$\frac{GM}{R^{2} }$

Explanation:

• Gravitational force is defined as the force of attraction between the two bodies in the universe. It is given as directly proportional to the product of masses of the bodies and inversely proportional to the square of distance between the bodies.

                                                    F ∝ m₁m₂

                                                    F ∝ $\frac{1}{r^{2} }$

by combining above equations we get

                                                  F = G$\frac{m_{1} m_{2} }{r^{2} }$               ................(1)

where,  m₁ and m₂ are the masses of two bodies

r = distance between two bodies

G = gravitational constant

• Gravitational force on Earth is defined as the force of attraction by which Earth attract any another body placed on it, known as Earth's gravitational force and is given as weight of the body

                                                     F = mg                .............................(2)

Then the gravitational force between Earth and another body of mass m is given as                                        F = G$\frac{Mm}{R^{2} }$             ...............................(3)

where, M = mass of Earth

R = radius of Earth

g = acceleration due to gravity

From equation (2) and (3)

=> mg = G$\frac{Mm}{R^{2} }$

=> g = $\frac{GM}{R^{2} }$

To know more about acceleration due to gravity, visit:

What do you mean by acceleration due to gravity? Write its numerical value and unit. Derive it’s unit from the formula g = GM /R2

https://brainly.in/question/1595444

What do you mean by acceleration due to gravity?

https://brainly.in/question/2073284