## Physics XI Content

# MASS OF EARTH

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MASS OF EARTH | |||

Consider a body of mass ‘m’ placed on the surface of the earth. Let the mass of the earth is ‘M_{e}’ and radius of the earth is ‘R_{e}’. Neglecting the radius of body if compared with that of the earth. | |||

Gravitational force of attraction between earth and body is | |||

F = G m M_{e}/ R_{e}^{2 }^{……..(1)} | |||

We know that the force of attraction of the earth on a body is equal to weight the weight of body. | |||

i.e | |||

F = W ……………………(2) | |||

therefore | |||

Comparing (1) and (2), we get, | |||

W = G m M_{e}/ R_{e}^{2 } | |||

But W = mg | |||

mg = G m M_{e}/ R_{e}^{2} | |||

org = G M _{e}/R_{e}^{2} | |||

orM_{e} = g x R_{e}^{2}/G | |||

From astronomical data: g= 9.8 m/s ^{2}R _{e }= 6.38 x 10^{6} mG = 6.67 x 10 ^{-11} N-m^{2}/kg^{2}Putting these values in the above equation. | |||

M_{e} = 9.8 (6.38 x 10^{6})^{2}/6.67 x 10^{-11}or | |||