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Calculate mass of the Earth from given d...

Calculate mass of the Earth from given data, Acceleration due to gravity `g = 9.81m//s^2`
Radius of the Earth `R_E = 6.37xx10^6 m`
` G = 6.67xx10^(-11) N m^2 //kg^2`

Text Solution

Verified by Experts

`g = (GM_E)/(R_E^2)`
` therefore M_E = (gR_E^2)/(G)`
` therefore M_E = (9.81 xx (6.37 xx 10^6)^2)/(6.67 xx 10^(-11)`
` therefore M_E = 5.97 xx 10^24 kg `
The value of g depends only on the properties of the Earth and does not depend on the mass of the object. This is exactly what Galileo had found from his experiments of dropping objects with different masses from the same height.
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