Q. Two stars of mass $m_{1}$ and $m_{2}$ are parts of a binary system. The radii of their orbits are $r_{1}$ and $r_{2}$ respectively, measured from the C.M. of the system. The magnitude of gravitational force $m_{1}$ exerts on $m_{2}$ 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
(a) Both the stars with same angular velocity $\omega$ around the centre of mass $(CM)$ in their respective orbits as shown in figure
The magnitude of gravitational force $m_{1}$ exerts on $m_{2}$ is $|F| = \frac{Gm_{1}m_{2}}{\left( r_{1} + r_{2} \right)^{2}}$
[image:8_image65.emf]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.