Maharashtra State BoardHSC Science (General) 11th
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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? - Physics

Sum

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)

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Solution

Given: M = 6 × 1024 kg, RE = 6400 km = 6.4 × 10m, 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.

Concept: Earth Satellites
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APPEARS IN

Balbharati Physics 11th Standard Maharashtra State Board
Chapter 5 Gravitation
Exercises | Q 4. (xii) | Page 99
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