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Question
Solve the following problem.
What is the gravitational potential due to the Earth at a point which is at a height of 2RE above the surface of the Earth?
(Mass of the Earth is 6 × 1024 kg, radius of the Earth = 6400 km and G = 6.67 × 10–11 N m2 kg–2)
Solution
Given: M = 6 × 1024 kg, RE = 6400 km = 6.4 × 106 m, G = 6.67 × 10–11 N m2/kg2, h = 2RE
To find: Gravitational potential (V)
Formula: V = -`"GM"/"r"`
Calculation: From formula,
V = `- "GM"/("R"_"E" + 2"R"_"E")`
`= - (6.67 xx 10^-11 xx 6 xx 10^24)/(3 xx 6.4 xx 10^6)`
`= -(6.67 xx 2)/6.4 xx 10^7`
= - 2.08 × 107 J kg-1
Negative sign indicates the attractive nature of gravitational potential.
Gravitational potential due to Earth will be 2.08 × 107 J kg-1 towards the centre of the Earth.
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