Acceleration Due To Gravity, Force, Important Topics, JEE Physics 2024

Acceleration Due to Gravity : We will study that the value of g is independent of the shape, size, mass, etc. of the body but depends upon mass and radius of the earth or planet due to which there is a gravity pull. When two bodies of different masses are allowed to fall from same height in vacuum, they reach the earth at the same time.

If the two bodies of same mass but of different volumes are allowed to fall from same height in air medium, they will not be reaching simultaneously. The body of smaller volume will reach the earth earlier than the other body, since the upward thrust due to air on the body of smaller volume will be less than that on the body of larger volume. A detailed discussion on how g varies with height, depth and the shape of the earth is provided with mathematical formulations.

Gravity, Force

Gravity : Earth attracts all bodies towards its center. This property of the earth is called ‘gravity’ and the force with which it attracts a body is called the ‘force of gravity’ acting on that body. Thus, when a body falls freely towards the earth’s surface, the force of gravity F produces an acceleration g in it given by.

This acceleration is called acceleration due to gravity. Its magnitude g is independent of the mass, size, shape and composition of the body. It is directed radially inward to the center of the earth. If in Newton’s law of gravitation one body (say earth) is taken as ‘reference body’, the force with which the reference body attracts any other body towards its center is called force due to gravity (of reference body) and the phenomenon ‘gravity’.

Now if the body is free to move, the force of gravity (of reference body) in accordance with Newton’s Second law will produce an acceleration in it. The acceleration produced in a body by the force of gravity of reference body (usually earth) is called acceleration due to gravity and is represented by g. If the reference body has mass M and radius R, the force on a body of mass m at the surface of reference body by Newton’s law of gravitation will be.

and if g is acceleration due to gravity of reference body on its surface, by Newton's Second law,

F = mg

It is independent of mass, shape, size, etc., of ‘falling body’, i.e. , a given reference body produces same acceleration in a light and a heavy falling body. When a body is dropped from a certain height above the ground it begins to fall towards the earth under gravity. The acceleration produced in the body due to gravity is called acceleration due to gravity. It is denoted by g . Its value close to the earth’s surface is 9.8 m / s ² . Suppose that the mass of the earth is M , its radius is R , then the force of attraction acting on a body of mass m close to the surface of earth is.

This expression is independent of m. If two bodies of different masses are allowed to fall freely, they will have the same acceleration, i.e. if they are allowed to fall from the same height, they will reach the earth simultaneously.

GRAVITY

Gravity is the force of attraction exerted by earth towards its center on a body lying on or near the surface of earth. Gravity is merely a special case of gravitation and is also called earth’s gravitational pull. For illustration, the force of attraction between two bodies on the surface of earth is the force of gravitation. but the force of attraction between each body and the earth is the force of gravity.

Force of gravity acting on a body is the measure of weight of the body. Thus, weight of a body is defined as the force of attraction exerted by the earth on the body towards its center.

Variation of g With Altitude

Variation of g With Altitude : As for an external point a spherical distribution of mass behaves as if the whole of its mass were concentrated at the center, i.e.,

Depth below the Surface of the Earth

Depth below the Surface of the Earth : Let an object of mass m is situated at a depth d below the earth’s surface. Its distance from the center of earth is ( d – R ). This mass is situated at the surface of the inner solid sphere and lies inside the outer spherical shell. According to Gauss theorem the gravitational force of attraction on a mass inside a spherical shell is always zero. Therefore, the object experiences gravitational attraction only due to the inner solid sphere. The mass of this sphere is,

Important Points

We can see from this equation that g ′ = 0 at d = R , i.e. acceleration due to gravity is zero at the center of

the earth. Thus, the variation in the value of g with r (the distance from the center of earth) is as shown in fig. 13.18.

For r ≤ R ,

as R – d = r or g ’ ∝ r

For r ≥ R ,

as R + d = r or g ’ ∝

Effect of Shape of Earth

Thus, we conclude that the value of g is least at the equator and maximum at the pole. It means, the value of acceleration due to gravity increases as we go from equator to the pole. At sea level, the value of g at pole is greater than its value at equator by 1.80 cm s ^–2 .