Question

(a) What do you understand by free fall? Derive an expression for acceleration due to gravity.

(b) Mass of earth is 81 times that of the moon, and its diameter is 3.6 times that of the moon. Compare the acceleration due to gravity on the earth and on the moon.

Answer 1

(a) When an object moves towards earth vertically under the effect of gravitational force only, its motion is said to be free fall.

Acceleration due to gravity

The gravitational force between an object and earth is given by

On putting values of mE and RE, the value of g at the surface of earth obtained is g = 9.8 m/sec.

(b) Let the mass of earth = m, Radius of earth = R_m

mass of the Moon = R_m

A radius of Moon = R_m

If acceleration due to earth is g and due to the moon is g_m then