Gravitation Question 368
Question: A system consists of two stars of equal masses that revolve in a circular orbit about a centre of mass midway between them. Orbital speed of each star is v and period is T. Find the mass M of each star (G is gravitational constant)
Options:
A) $ [\frac{2Gv^{3}}{\pi T}] $
B) $ [\frac{v^{3}T}{\pi G}] $
C) $ [\frac{v^{3}T}{2\pi G}] $
D) $ [\frac{2Tv^{3}}{\pi G}] $
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Answer:
Correct Answer: D
Solution:
-
$ [\frac{Mv^{2}}{R}=\frac{GM^{2}}{4R^{2}}\Rightarrow M=\frac{4Rv^{2}}{G}] $
$ [v=\frac{2\pi R}{T},,,,,,,,,,,,R=\frac{vT}{2\pi },,,M=\frac{v^{3}T2}{\pi G}] $
