At what height from the surface of earth the gravitation potential and the value of g are - 5.4 × 107 J kg-2 and 6.0 ms-2 respectively ? Take the radius of earth as 6400 km :

Question

At what height from the surface of earth the gravitation potential and the value of g are - 5.4 × 107 J kg-2 and 6.0 ms-2 respectively ? Take the radius of earth as 6400 km : (A) 1600 km (B) 1400 km (C) 2000 km (D) 2600 km

Tardigrade Admin · Accepted Answer

V = (-GM/R +h) = -5.4 × 107 ....(1) and g = (GM/(R + h)2) = 6 ......(2) dividing (1) and (2) ⇒ (5.4 × 107/(R + h)) = 6 ⇒ R + h = 9000 km so h = 2600 km

Q. At what height from the surface of earth the gravitation potential and the value of g are $- 5.4 \times 1 0^{7} J k g^{- 2}$ and $6.0 m s^{- 2}$ respectively ? Take the radius of earth as $6400 km$ :

1600 km

1400 km

2000 km

2600 km

$V = \frac{- GM}{R + h} = - 5.4 \times 1 0^{7}$ ....(1)
and $g = \frac{GM}{( R + h ) ^{2}} = 6$ ......(2)
dividing (1) and (2)
$\Rightarrow \frac{5.4 \times 1 0 ^{7}}{( R + h )} = 6$
$\Rightarrow R + h = 9000 km$ so $h = 2600 km$

Q. At what height from the surface of earth the gravitation potential and the value of g are −5.4×107Jkg−2 and 6.0ms−2 respectively ? Take the radius of earth as 6400km :