At what height from the surface of earth the gravitation potential and the value of g are - 5.4 × 10 ^ 7 Jk g ^ - 2 and 6.0m s ^ - 2 respectively? Take the radius of earth as 6400 km :

Correct answer: A. 2600 km V = (GM)/(R + h) = - 5.4 × 10 ^ 7 g = GM (R + h) ^ 2 = 6 ∴ (5.4)/(6) × 10 ^ 7 = R + h ∴ 9 × 10 ^ 6 = 6.4 × 10 ^ 6 + h ∴ h = 2600km

NEET 2016

Exam: NEET
Year: 2016
Subject: Physics
Chapter: Gravitation

NEET 2016 · Physics · Gravitation

At what height from the surface of earth the gravitation potential...

At what height from the surface of earth the gravitation potential and the value of g are

- 5.4 \times {10}^{7}Jk{g}^{- 2}

and

6.0m{s}^{- 2}

respectively? Take the radius of earth as

6400 km

Options

A $2600 km$
B $1600 km$
C $1400 km$
D $2000 km$

Correct answer

A. $2600 km$

Step-by-step solution

V = \dfrac{GM}{R + h} = - 5.4 \times {10}^{7}

g = \dfrac{GM}{{\left(R + h\right)}^{2}} = 6

∴ \dfrac{5.4}{6} \times {10}^{7} = R + h

∴ 9 \times {10}^{6} = 6.4 \times {10}^{6} + h

∴ h = 2600km

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