Question

The gravitational field intensity at a point $10,000 \,km$ from the centre of the earth is $4.8\, N \,kg^{-1}$. The gravitational potential at that point is

• A. $-4.8 \times 10^7\, J \,kg^{-1}$
• B. $-2.4 \times 10^7\, J \,kg^{-1}$
• C. $4.8 \times 10^6\, J \,kg^{-1}$
• D. $3.6 \times 10^6\, J \,kg^{-1}$

Answer 1

Answer: (A)

Gravitational field intensity, $E = \frac{GM}{R^{2}}$
Gravitational potential, $V =-\frac{GM}{R}$
$\therefore \frac{V}{E} = -R$
$\therefore \frac{V}{E} = -R$
or $V= -ER = -4.8 \times 10,000 \times 10^{3}$
$= -4.8 \times 10^{7}\, J \,kg^{-1}$