Two objects, each of mass m, are distance x apart and experience a gravitational force F. If the mass of both objects is doubles and their separation is halved then what is the gravitational force between them?

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Sorry about that.

This is actually a multiple choice question, with the options being:
(A) F/4
(B) 2F
(C) 8F
(D) 16F

I thought that by doubling the masses, the force is also doubled, and then by halfing the distance the force is doubles again, hence I think it is 8F, but the answer is 16F and I do not know how it is 16F

The formula for the gravitational force is as follows:

F=\frac{Gm_1m_2}{r^2}

G is a constant. m_1 is the mass of the first object, m_2 that of the second object and r the distance between them. Can you find the answer now?

Hope it helped! :)

Remember that the general formula for gravitational attraction is:


F = \frac {G*M_1*M_2} {R^2}


where M_1 and M_2 are the masses of the two objects, and R is the distance between them.

So if M_1 doubles the force goes up by a factor 2, and if M_2 also doubles then force goes up by another factor of 2. So the numerator is now 4 times greater than the original. Then when R is cut in half the new R^2 is 1/4 the value of the original R^2 . So the ratio of the two forces, taking all this into account, is 4 divided by 1/4, or 16.

You can also do it more rigorously this way:


F_1 = \frac {G* M_1 * M_2} {R^2} \\
F_2 = \frac {G * 2 M_1 * 2 M_2 } {(\frac 1 2 R)^2} \\
\frac {F_2} {F_1} = \frac {2*2} {(\frac 1 2 ) ^2} = 16

G=f(x)square/8m1.8m2

Can anybody tell me if I'm doing this right?

My equation is:

F= {[m1(2)] * [m2(2)]} / x^2

Can anybody tell me if I'm doing this right?

My equation is:

F= {[m1(2)] * [m2(2)]} / x^2

You left out the constant G, which is required in order to get the units right. Also, what is the meaning of the notation "m1(2)" and "m2(2)"? The correct formula is:

F = G*M1*M2/(x^2)

Where M1 is the mass of object one and M2 is the mass of object 2, and x is the distance between their centers of mass.