CBSE Class 11-science Answered

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.

Numerical Value of Acceleration due to Gravity on Earth

Gravitational Constant (G) = 6.6734 x 10^-11 Nm²/kg²

Mass of the Earth (M_e) = 6 x 10²⁴ kg

Radius of the Earth (R_e) = 6.4 x 10⁶ m