Question

Two bodies of mass $M$ and $m$ are revolving around the centre of mass of the system in circular orbit of radii $R$ and $r$ respectively due to mutual interaction. Which of the following formula is applicable?

• A. $\frac{GMm}{(R+r{)}^2}=m{\omega }^{2}r$
• B. $\frac{GMm}{R^2}=m{\omega }^{2}r$
• C. $\frac{GMm}{r^2}=m{\omega }^{2}r$
• D. $\frac{GMm}{R^2+r^2}=m{\omega }^{2}r$

Answer 1

The correct option is A $\frac{GMm}{(R+r{)}^2}=m{\omega }^{2}r$

Two bodies of mass $M$ and $m$ are revolving around the centre of mass of the system in circular orbit of radii $R$ and $r$ respectively.

At equilibrium, $F_G=F_c$

As distance between the two bodies is (R+r) $⟹F_G=\frac{GMm}{(R+r{)}^2}$

$F_c=\frac{m{v}^2}{r}=mr{w}^2$

Thus, $\frac{GMm}{(R+r{)}^2}=mr{w}^2$