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

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 × 107 J kg-1 (B) -2.4 × 107 J kg-1 (C) 4.8 × 106 J kg-1 (D) 3.6 × 106 J kg-1

Tardigrade Admin · Accepted Answer

Gravitational field intensity, E = (GM/R2) Gravitational potential, V =-(GM/R) ∴ (V/E) = -R ∴ (V/E) = -R or V= -ER = -4.8 × 10,000 × 103 = -4.8 × 107 J kg-1

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

$- 4.8 \times 1 0^{7} J k g^{- 1}$

$- 2.4 \times 1 0^{7} J k g^{- 1}$

$4.8 \times 1 0^{6} J k g^{- 1}$

$3.6 \times 1 0^{6} J k g^{- 1}$

Gravitational field intensity, $E = \frac{GM}{R ^{2}}$
Gravitational potential, $V = - \frac{GM}{R}$
$∴ \frac{V}{E} = - R$
$∴ \frac{V}{E} = - R$
or $V = - ER = - 4.8 \times 10, 000 \times 1 0^{3}$
$= - 4.8 \times 1 0^{7} J k g^{- 1}$

Q. The gravitational field intensity at a point 10,000km from the centre of the earth is 4.8Nkg−1. The gravitational potential at that point is

−4.8×107Jkg−1

−2.4×107Jkg−1

4.8×106Jkg−1

3.6×106Jkg−1