Two satellites 'A' and 'B' of masses ten and twenty metric tons revolve around the Earth at two different height `h_(1) and h_(2)` from the surface of the Earth. If earth's gravitational pull on these two satellites at these heights is equal, then find the ratio of their distances from the centre of the Earth . (Radius of the Earth = 6400 km)

Explanation

Given that, the weights of the two satellites A and B are equal at their heights `h_(1) and h_(2)`, respectively. `w_(1) = w_(2)`
Let, acceleration due to gravity at the two satellites be `'g_(1)' and 'g_(2)'`, respectively.
`rArr m_(1)g_(1) = m_(2)g_(2)`
`rArr ("10 metric tonne") (GM_(E))/((R + h_(1))^(2))`
`= ("20 metric tonne") (GM_(E))/((R + h_(2))^(2))`
`g = (GM_(E))/((R + h)^(2)) rArr ((R + h_(1))^(2))/((R + h_(2)))=(1)/(2)`
`rArr ((R + h_(1)))/((R + h_(2)))=(1)/(sqrt(2))`
Therefore, the ratio of their distances from the centre of the Earth `= 1 : sqrt(2)`