Acceleration Due to Gravity

Abstract

Acceleration due to gravity is the acceleration gained by an object due to gravitational force. Its SI unit is m/s 2. It has both magnitude and direction; hence, it's a vector quantity. Acceleration due to gravity is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s 2. Acceleration Due to Gravity-Formula, Unit and Values Acceleration Due to Gravity (g) Symbol g Dimensional Formula M 0 L 1 T-2 SI Unit ms-2 Formula g = GM/r 2 Values of g in SI 9.806 ms-2 Values of g in CGS 980 cm s-2 KEYWORDS-Acceleration Due to Gravity, gravitational force, surface of the earth, magnitude and direction I.INTRODUCTION Gravity is the force with which the earth attracts a body towards its centre. Let us consider two bodies of masses, m a and m b. Under the application of equal forces on two bodies, the force in terms of mass is given by m b = m a [a A /a B ]; this is called an inertial mass of a body. Under the gravitational influence on two bodies,[1,2]  F A = GMm A /r 2 ,  F B = GMm B /r 2 ,[3]  m B = [F B /F A ] × m A The above mass is called a gravitational mass of a body. According to the principle of equivalence, the inertial mass and gravitational mass are identical. We will be using this while deriving acceleration due to the gravity given below.Suppose a body [test mass (m)] is dropped from a height 'h' above the surface of the earth [source mass (M)]; it begins to move downwards with an increase in velocity as it reaches close to the earth's surface.We know that the velocity of an object changes only under the action of a force; in this case, the force is provided by gravity.Under the action of gravitational force, the body begins to accelerate toward the earth's centre, which is at a distance 'r' from the test mass.[5,7,8]