**Introduction About Value of g:**

**Mass** is a measure of how much matter an object contains, while **weight** is a measure of the force of gravity on the object. An object has the same composition, and therefore mass, regardless of its location.watch Introduction About Value of g to learn more.

**The Weight of the Body Depends on the Value of g:**

Consider an object of mass m lying on or near the surface of the Earth. Let M_{e} be the mass of the Earth and R_{e} be its radius i.e., R_{e} is the distance between the object and the centre of the Earth.

According to Newton’s law of gravitation, the force of attraction (F) between the Earth and the object is

A body of mass m lying on the surface of the Earth.

According to Newton’s second law of motion this force produces an acceleration (g) in the object.

F=ma (a=g)

F=mg

Substituting the value of F in eq (2) we get,

From eq (3) it is very clear that acceleration due to gravity does not depend on the mass m of the object. It only depends on the mass of the Earth (M_{e}) and the distance from the centre of the Earth to the object.Consider an object of mass m lying on or near the surface of the Earth. Let M_{e} be the mass of the Earth and R_{e} be its radius i.e., R_{e} is the distance between the object and the centre of the Earth.

According to Newton’s law of gravitation, the force of attraction (F) between the Earth and the object is

A Body of Mass m Lying on the Surface of the Earth

According to Newton’s second law of motion this force produces an acceleration (g) in the object.

F = ma (a = g)

F = mg

Substituting the value of F in equation (2) we get,

From equation (3) it is very clear that acceleration due to gravity does not depend on the mass m of the object. It only depends on the mass of the Earth (M_{e}) and the distance from the centre of the Earth to the object.

The expression for acceleration due to gravity is

Where G is the universal gravitational constant, M is the mass of the celestial body which produces acceleration in a body and R is the radius of the celestial body.

The equation for g shows that the value of acceleration due to gravity depends on the mass and radius of the celestial body and hence will be different for different celestial bodies.

Let us now derive a relation between the acceleration due to gravity on moon (g_{m}) and acceleration due to gravity on Earth (g_{e}).

Where M_{e} and R_{e} are the mass and radius of the Earth respectively.

Where M_{m} and R_{m} are the mass and radius of the moon respectively.

Divide equation (1) by equation (2)

We know that mass of the Earth is 100 times that of the moon and its radius is four times that of the moon.

i.e.,

Which means that acceleration due to gravity on moon is 1/6^{th} that on the Earth.

Useful for CBSE, ICSE, NCERT & International Students

Grade :9

Subject : Physics

Lesson : Gravitation

Topic:Value of g

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