If the Earth were a homogenous sphere of wood of density 800 kg/`m^(3)`. What would be (i)the acceleration due to gravity on the Earth's surface ? (ii) the critical velocity of a satellite orbiting close to its surface ?

Explanation

Data : `p = 800 kg//m^(3) , G = 6.67 xx 10^(-11) N.m^(2)//Kg^(2)R_(E) = 6.4 xx 10^(6)` m
(i) ` g = GM_(E)//R_(E)^(2)`
Assuming the Earth to be a homogenous sphere of density p.
` M_(E) = 4/3 piR_(E)^(3)p`
Then , the surface gravity on a wooden Earth .
` g = (G (4/3 piR_(E)^(3)p))/(R_(E)^(2)) = 4/3piGR_(E)p`
` 4/3 (3.142) (6.67 xx 10^(-110 ) (6.4 xx 10^(6)) (800) `
` = 1.431 m//s^(2)`
(ii) The critical velocity close the the surface of the wooden Earth.
` v_(c0= sqrt(gR_(E)) = sqrt(1.431 xx 6.4xx10^(6))`
`3.026 xx 10^(3) m//s`