Question

Find the Gravitational Potential at a point on the earth’s surface. Take mass of earth as 5.98X 10 24 kg, its radius as 6.38 X 10 6 m and G = 6.67 X 10 – 11 Nm2
kg – 2.

Answer 1

Given,

Mass of Earth = 5.98 x 10^24 Kg

Radius of Earth = 6.38 x 10^6 m

Gravitational Constant = 6.67 x 10^-11 Nm^2kg^-2

Now,

$\impliesGravitational \: Potential = \dfrac{-GM}{R}$

$\implies U_{g} = \dfrac{-6.67\times{10}^{-11} \times 5.98 \times{10}^{24}}{6.38\times{10}^{6}}$

$\implies U_{g} = \dfrac{-39.8\times{10}^{13}}{6.38\times{10}^{6}}$


$\implies U_{g} = -6.23\times{10}^{7}$

$\implies U_{g} = -62.3 \times {10}^{6} J{Kg}^{-1}$