Question

A relationship exists between gravity, mass, and distance. The greater the mass of the objects, the greater the gravitational force between them. The greater the distance between the objects, the weaker the gravitational force between them. Which of these objects would have the greatest gravitational force between them? two objects, each with a mass of 10 kg, separated by a distance of 10 m two objects, each with a mass of 20 kg, separated by a distance of 10 m two objects, each with a mass of 20 kg, separated by a distance of 15 m two objects, each with a mass of 10 kg, separated by a distance of 15 m

Answer 1

Answer would be :
2 objects both with mass of 20kg and distance of 10m

Because mass is greater than the rest and also distance is the shortest which means there will be a bigger gravitational force compared to the rest

Answer 2

The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the distance between the two objects. hence the Gravitational force is given as

F = k (product of masses)/(distance)² where k = constant

when mass of each object = 10 kg , distance = 10 m

F = k (10 x 10)/(10)² = k

when mass of each object = 20 kg , distance = 10 m

F = k (20 x 20)/(10)² = k (400/100) = 4k

when mass of each object = 20 kg , distance = 15 m

F = k (20 x 20)/(15)² = (1.8) k

when mass of each object = 10 kg , distance = 15 m

F = k (10 x 10)/(15)² = (0.44) k

hence the force is greatest when

two objects, each with a mass of 20 kg, separated by a distance of 10 m