Maharashtra State BoardHSC Science (General) 11th

Solve the following problem. Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km - Physics

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Sum

Solve the following problem.

Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s2.

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Solution

Given: M = 6 × 1024 kg, R = 6400 km = 6.4 × 106 m, g = 9.8 m/s2

To find: Gravitational constant (G)

Formula: g = `"GM"/"R"^2`

Calculation: From formula,

G = `"gR"^2/"M"`

G = `(9.8 xx (6.4 xx 10^6)^2)/(6 xx 10^24) = (401.4 xx 10^12)/(6 xx 10^24)`

∴ G = 6.69 × 10-11 Nm2/kg2

The value of gravitational constant is 6.69 × 10-11 Nm2/kg.

Concept: Earth Satellites
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APPEARS IN

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