(a) Is the acceleration due to gravity of earth ‘g’ a constant? Discuss.
(b) Calculate the acceleration due to gravity on the surface of a satellite having a mass of 7.4 x 1022 kg and a radius of 1.74 x 106 m (G = 6.7 x 10-11 Nm2/kg2). Which satellite do you think it could be?
(a) No, the value of acceleration due to gravity (g) is not constant at all the places on the surface of the earth. Since the radius of the earth is minimum at the poles and maximum at the equator, the value of g is maximum at the poles and minimum at the equator. As we go up from the surface of the earth, the distance from the centre of the earth increases and hence the value of g decreases. The value of g also decreases as we go down inside the earth.
(b) Acceleration due to gravity.
g = \(G \times \frac{M}{R^2}\)
Mass, M = 7.4 x 1022 kg
Radius, R = 1.74 x 106 m
Gravitational constant, G = 6.7 x 10-11 Nm2/kg2
g = 6.7 x 10-11 x \(\frac{7.4 \times 10^{22}}{(1.74 \times 10^6)^2}\)
g = \(\frac{6.7 \times 7.4}{1.74 \times 1.74 \times 10}\)
g = 1.637 m/s
As the value of g = 1.637 m/s2, which is one sixth the value of g on earth, the satellite could be moon.