Q. Two stars of mass $m_{1}$ and $m_{2}$ are part of a binary star system. The radii of their orbits are $r_{1}$ and $r_{2}$ respectively, measured from the C.M. of the system. The magnitude of acceleration of $m_{1}$ is
A) $\frac{m_{1}m_{2}G}{\left( r_{1} + r_{2} \right)^{2}}$
B) $\frac{m_{1}G}{\left( r_{1} + r_{2} \right)^{2}}$
C) $\frac{m_{2}G}{\left( r_{1} + r_{2} \right)^{2}}$
D) $\frac{(m_{1} + m_{2})}{\left( r_{1} + r_{2} \right)^{2}}$
Explanation
(c) Force of attraction between two stars
$F = \frac{Gm_{1}m_{2}}{\left( r_{1} + r_{2} \right)^{2}}$
Acceleration $= \frac{F}{m_{1}} = \frac{Gm_{2}}{\left( r_{1} + r_{2} \right)^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.