Question #173955

(i)           The resultant gravitational force exerted upon the body at this point is zero. Calculate the distance R of the body from the centre of the Earth given that

r = 3.9 × 107 m and ME = 81 MM

1
Expert's answer
2021-03-29T09:04:47-0400

The two forces are in equilibrium, which means the force of attraction between the earth and body (which is r = 3.9 × 107 away from Earth) is the same as the force between the body and mass MM at distance R:


FE=FM, GMEmr2=GMMmR2, R=rMMME=3.9107181=4.3106 m.F_E=F_M,\\\space\\ G\frac{M_Em}{r^2}=G\frac{M_Mm}{R^2},\\\space\\ R=r\sqrt{\frac{M_M}{M_E}}=3.9·10^7\sqrt{\frac{1}{81}}=4.3·10^6\text{ m}.

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