Question

If the masses of two planets doubles and the distance between them reduces by half, the force between them would be

Answer 1

let

m₁= mass of the planet 1^st

m₂= mass of the second planet

d= distance between the planets

force between two planets is

F = (G m₁ m₂ )/(d² )

now the masses of the planets  becomes doubled and distance is reduce to half then

"m₁ " becomes "2m₁ " and "m₂ " becomes "2m₂" and "d" becomes "d/2" then force becomes

F' = (G 2m₁2m₂) / (d/2)² = 4Gm₁m₂ / ( d²/4)

F' = 16(G m₁ m₂ )/(d² ) = 16F

the force between them would be BECOMES 16 TIMES OF INITIAL FORCE