Question

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

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

Answer 1

Answer: (A)

$-4.8\times {10}^{7}Jk{g}^{-1}$

Gravitational field intensity, $E=\frac{GM}{R^2}$
Gravitational potential, $V=\frac{GM}{R}$
$\therefore \frac{V}{E}=-R$

Given data

Center of the earth $E=4.8Nk{g}^{-1}$

$-E=-4.8K{g}^{-1}$

Gravitaional field intensity $R=10,000Km$

or $V=-ER=-4.8\times 10,000\times {10}^3$

$=-4.8\times {10}^{7}JK{g}^{-1}$