Question

Suppose that two objects attract each other with a gravitational force of 16 units. if the mass of object one was doubled, and if the distance between the objects was tripled, then what would be the new force of attraction?

Answer 1

Answer: F = 4 units

Step-by-step explanation:

If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (22). The new force is then 1/4 of the original 16 units.

F = (16 units ) / 4 = 4 units

Answer 2

Answer: 3.5units

Step-by-step explanation:

Gravitational force existing between the two masses is directly proportional to the product of their masses and inversely proportional to the square of the distances between the masses.

Mathematically, F = GMm/r^2

G is the gravitational constant

M and m are the masses

r is the distance between the masses.

If the force of attraction between the masses is 16units, it becomes,

16 = GMm/r^2... (1)

If the mass of object 1 is doubled and distance tripled, we will have

F= G(2M)m/(3r)^2

F=2GMm/9r^2... (2)

Solving eqn 1 and 2 to get the new Force

Dividing eqn 1 by 2, we have

16/F = GMm/r^2 ÷ 2GMm/9r^2

16/F = GMm×9r^2/r^2×2GMm

16/F = 9/2(upon cancelation)

Cross multiplying we have

9F=32

F= 32/9

F= 3.5units