Question

Two particles of equal mass revolve in a circle of radius R under the influence of mutual gravitational attraction. Calculate the velocity of each particle.​

Answer 1

Answer: $\frac{\sqrt{Gm} }{2\sqrt{R} }$

Explanation: Net force= mass * acceleration

Let mass of each particle be m. The 2 particles are diametrically opposite. Distance between them = 2R

Here net force = gravitational force on one mass by another = G$m^{2}$ / $(2R)^{2}$

Acceleration of each particle = Centripetal acceleration = $\frac{v^{2} }{R}$

F = ma

G$m^{2}$ / $(2R)^{2}$ = m *  $\frac{v^{2} }{R}$

$v^{2}$ = G$m^{2}$/ 4$R^{2}$ * R/m = Gm / 4R

Taking square root,

v = $\frac{\sqrt{Gm} }{2\sqrt{R} }$