Question

IS ANYONE GENIUS HERE TO SOLVE IT

Answer 1

let x be the height from the surface of the moon where value of 'g' at that height is equal to the value of 'g' at height 57600 km above earth surface

we have
ME = 6 × 10 ^ 24 kg
MM = 7.3 × 10 ^ 22 kg
RE = 6400 km
RM = 1740 km

now value of 'g' at height 57600 km from the surface of earth
= G × ME / (RE + 57600) ^ 2
= 6.673 × 10 ^ -11 Nm^2 kg^-2 × 6 × 10 ^ 24 kg / (6400000 m + 57600000 m) ^ 2
= 0.0977490234 ms^-2

since
value of 'g' on moon = G × MM / (RM + x) ^ 2
= 6.673 × 10 ^ -11 × 7.3 × 10 ^ 22 / (1740000 + x) ^ 2
=> 0.0977490234 = 6.673 × 10 ^ -11 × 7.3 × 10 ^ 22 / (1740000 + x) ^ 2

therefore x = 68853.7 km
hence at the height of 68853.7 km the value of 'g' is equal to the value of 'g' at height 57600 km above earth surface.

Answer 2

here is your answer read it carefully surely you will understand