Question

Consider two solid uniform spherical objects of the same density $\rho$. One has a radius $R$ and the other has a radius $2R$. They are in outer space where the gravitational fields from other objects are negligible. If the spheres are placed in contact with each other, then what is the gravitational force of attraction between them?

• A. $G\pi^2\rho^4$
• B. $\frac{128}{81} G\pi^2R^4 \rho^2$
• C. $\frac{128}{81}G\pi^2$
• D. $\frac{128}{87} \pi R^2 G$

Answer 1

Answer: (B)

$m_1 = \frac{4}{3} \pi R^3\rho, m_2 = \frac{4}{3} \pi(2R)^3 \rho,$
Distance between centres of two spherical objects,
$r = 3R$.
$F = \frac{Gm_1m_2}{r^2} = G(\frac{4}{3} \pi R^3 \rho)(8\times \frac{4}{3} \pi R^2\rho) \times \frac{1}{(3R)^2}$
$ = \frac{128}{81} G\pi^2 R^4 \rho^2$