Find the height from the surface of the moon where the value of 'g' is equal to the value of 'g' at a height of 57,600 km from the surface of the Earth.
(Take, mass of the Earth, `M_(E) = 6 xx 10^(24)` kg, Mass of the moon, `M_(m) = 7.3 xx 10^(22)` kg, radius of the Earth, `R_(E) = 6400` and radius of the moon, `R_(m) = 1740 km`)

Explanation

(i) (1.) The value of acceleration due to gravity at a height 'h' is given by, `g^(1)`
`= (GM_(m))/((R + h)^(2))`
(2.) The value of `g^(1)` is equal height `h_(E)` from the surface of the Earth `h_(m)` from the surface of the moon.
`rArr g^(1) = (GM_(E))/((R_(E) + h_(E))^(2)) = (GM_(m))/((R_(m) + h_(E))^(2))`
Substitute the values of `M_(E), M_(m), R_(E), h_(E), R_(m)` and find the value of `h_(m)` from equation (2).
(ii) 5300 km