It is the force of attraction exerted by earth towards its centre on a body lying on or near the surface of the earth. Gravity is the measure of the weight of the body.

The weight of a body of mass m = mass X acceleration due to gravity = mg.

The unit of weight of a body will be the same as those of force.

### Acceleration due to gravity (g):

It is defined as the acceleration set up in a body while falling freely under the effect of gravity alone. It is a vector quantity. The value of g changes with height, depth, rotation of earth the value of g is zero at the centre of the earth. The value of g on the surface of the earth is 9.8ms^{-2}.

The acceleration due to gravity (g) is related with gravitational constant (G) by the relation,

where M and R are the mass and radius of the earth.

**Explanation**: The force on the mass m at P has a magnitude

The mass m is a mine located at a depth d below the surface of the Earth of mass M_{E} and radius R_{E}. We treat the Earth to be spherically symmetric.

We assume that the entire earth is of uniform density and hence its mass is

where M_{E} is the mass of the earth R_{E} is its radius and ρ is the density. On the other hand, the mass of the sphere M_{r} of radius r is

and hence

If the mass m is situated on the surface of earth, then r = R_{E} and the gravitational force on it is,

The acceleration experienced by the mass m, which is usually denoted by the symbol *g *is related to F by Newton’s 2nd law by relation F = m*g*. Thus

**Variation of acceleration due to gravity****Effect of altitude**

The first is valid when h is comparable with R and the second relation is valid when h << R.

The value of g decreases with increase in h.

**Effect of depth**

The acceleration due to gravity decreases with increase in depth d and becomes zero at the centre of the earth.

**Effect of rotation of earth**

The acceleration due to gravity on equator decreases on account of rotation of the earth and increase with the increase in latitude of a place.

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