Question

derive expression on acceleration due to gravity

Answer 1

Dear Student, Force acting on a body due to gravity is given by, f = mg Where f is the force acting on the body, g is the acceleration due to gravity, m is mass of the body. According to the universal law of gravitation, f = GmM/(r+h)2 Where, f = force between two bodies, G = universal gravitational constant (6.67×10-11 Nm2/kg2) m = mass of the object, M = mass of the earth, r = radius of the earth. h = height at which the body is from the surface of the earth. As the height (h) is negligibly small compared to the radius of the earth we re-frame the equation as follows, f = GmM/r2 Now equating both the expressions, mg = GmM/r2 ⇒ g = GM/r2 Therefore, the formula of acceleration due to gravity is given by, g = GM/r2 Regards