At what height from the surface of earth the gravitation potential and the value of g are - 5.4 × 107 J kg ⁻¹ and 6.0 m s ⁻² respectively? Take the radius of earth as 6400 km. (a) 1400 km (b) 2000 km (c) 2600 km (d) 1600 km

Answer: (c). V = -GM/r and g = GM/r², so r = |V|/g. r = (5.4×10⁷)/(6.0) = 9×10⁶ m = 9000 km h = r - R = 9000 - 6400 = 2600 km So the answer is (c) 2600 km.

At what height from the surface of earth the gravitation potential… | NEET 2016 (Phase 1)

Q25NEET 2016 · PHASE 1Medium

Gravitational Potential & Energy

At what height from the surface of earth the gravitation potential and the value of g are $-$ 5.4 $\times$ 107 J kg ${}^{-1}$ and 6.0 m s ${}^{-2}$ respectively? Take the radius of earth as 6400 km.

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Answer: (c)

$V = -\frac{GM}{r}$ and $g = \frac{GM}{r^2}$ , so $r = \frac{|V|}{g}$ .
$r = \frac{5.4\times10^7}{6.0} = 9\times10^6\ \text{m} = 9000\ \text{km}$
$h = r - R = 9000 - 6400 = 2600\ \text{km}$
So the answer is (c) 2600 km.

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