4.1 Introduction

4.2 Gravitational forces

Points to Note

**Force**

Force is an interaction between two objects.

Force is exerted by an object A on another object B.

Force is a vector quantity. Hence if two or more forces act on a particle, we can find the resultant force using laws of vector addition.

The SI unit for measuring the force is called a newton.

**Newton's third law of motion**

If a body A exerts a force

**F**on another body B, then B exerts a force

**-F**on A,the two forces acting along the same line.

**Gravitational force**

Any two bodies attract each other by virtue of their masses.

The force of attraction between two point masses is

F = Gm1m2/r²

where m1 and m2 are the masses of the particles and r is the distance between them.

G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²

The above rule was given for point masses. But it is analytically found that the gravitational force exerted by a spherically symmetric body of mass m1 on another such body of mass m2 kept outside the first body is Gm1m2/r² where r is the distance between the centres of such bodies.

Thus, for the calculation of gravitational force between two spherically symmetric bodies, they can be treated as point masses placed at their centres.

Gravitational force on small bodies by the earth

For earth, the value of radius R and mass M are 6400 km and 6 x 10^24 kg respectively. Hence, the force exerted by earth on a particle of mass m kept at its surface is, F = GMm/R². The direction of this force is towards the centre of the earth.

The quantity GM/R² is a constant and has the dimensions of acceleration.

It is called acceleration due to gravity and is denoted by letter g.

Hence, g and G are different.

Value of g is approximately 9.8 m/s².

In calculations, we often use 10 m/s².

Force exerted on a small body of mass m, kept near the earth's surface is mg in the vertically downward direction.

Gravitational constant is so small that the gravitational force becomes appreciable only when one of the masses has a very large mass.

HC Verma gives the example of Force exerted by a body of 10 kg on another body of 10 kg when they are separted by a distance of 0.5 m. The force comes out to be 2.7*10^-8 N which can hold only 3 microgram. Such forces can be neglected in practice.

Hence we consider only gravitational force exerted by earth.

Formulas

1. F = Gm1m2/r²

where m1 and m2 are the masses of the particles and r is the distance between them.

G is a universal constant having the value 6.67 x 10^-11 N-m²/kg²

2. Force exerted by earth on a particle of mass m kept at its surface is, F = gm/R².

g = approximately 9.8 m/s².

In calculations, we often use 10 m/s²

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