Question

Two small objects, with masses m and m, are originally a distance r apart, and the gravitational force on each one has magnitude f. the second object has its mass changed to 2m, and the distance is changed to r/4. what is the magnitude of the new gravitational force?

Answer 1

32f. That's because the force is directly proportional to the product of the masses and inversely proportional to the square of the distance. So you get 2•(1/1/4)^2=2•16=32

Answer 2

New gravitational force, F' = 32 F

Step-by-step explanation:

The gravitational force acting on two objects that are separated by a distance r between them is given by :

`F=G(mM)/(r^2)`

m is the mass of object 1

M is the mass of object 2

Now, the second object has its mass changed to 2m, and distance is changed to r/4. So, the gravitational force becomes :

`F'=G(m* 2M)/((r/4)^2)`

`F'=32* (GmM)/(r^2)`

`F'=32* F`

So, the magnitude of the new gravitational force is 32 times the previous force. Hence, this is the required solution.