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- Homework Statement
- two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to ( R = radius of each sphere)

- Relevant Equations
- $$F= \frac{Gm_1m_2} {r^2} $$

$$ m=\frac{4}{3}\pi R^3\rho $$

I recently encountered this problem on a test where the solution for the above problem was given as follows:

$$F= \frac{Gm_1m_2} {r^2} $$ (1)

but

$$ m=\frac{4}{3}\pi R^3 $$

substituting in equation (1)

$$F= \frac{{G(\frac{4}{3}\pi R^3\rho})^2 }{2R^2} $$

where r=radii of the two spheres

m=mass of the two spheres

##\rho ##=density of the two spheres

solving further we get

$$F \alpha \frac{R^6}{R^2}$$

Therefore,

$$F \alpha R^4$$

But isn't gravity an inverse square force. An explanation I read in a book previously said that

$$F \alpha R^4$$

cannot be correct because it is against the basic concept which is more important than a numerical value and that an inverse square law is fundamental and gravitational force is for masses and not for densities.

This makes more sense to me than the solution provided for the test but I am still really confused as to which explanation is right

$$F= \frac{Gm_1m_2} {r^2} $$ (1)

but

$$ m=\frac{4}{3}\pi R^3 $$

substituting in equation (1)

$$F= \frac{{G(\frac{4}{3}\pi R^3\rho})^2 }{2R^2} $$

where r=radii of the two spheres

m=mass of the two spheres

##\rho ##=density of the two spheres

solving further we get

$$F \alpha \frac{R^6}{R^2}$$

Therefore,

$$F \alpha R^4$$

But isn't gravity an inverse square force. An explanation I read in a book previously said that

$$F \alpha R^4$$

cannot be correct because it is against the basic concept which is more important than a numerical value and that an inverse square law is fundamental and gravitational force is for masses and not for densities.

This makes more sense to me than the solution provided for the test but I am still really confused as to which explanation is right