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?

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

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Muscardinus Muscardinus · Answer 2 · 2019-10-15T08:56:13+02:00

Answer:

New gravitational force, F' = 32 F

Explanation:

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

[tex]F=G\dfrac{mM}{r^2}[/tex]

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 :

[tex]F'=G\dfrac{m\times 2M}{(r/4)^2}[/tex]

[tex]F'=32\times \dfrac{GmM}{r^2}[/tex]

[tex]F'=32\times F[/tex]

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