KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 100 of 120

Marks: +1, -0

A star of mass M (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a circular orbit. The velocity of the star with respect to the center of mass of the star-planet system is shown below :

The radius of the planet's orbit is closest to
(1 A. U. = Earth-Sun distance)

0.004 A. U.
0.008 A.U.
0.004 A.U.
0.12 A.U

Validate

Solution:

T ^2 = {4π^2}/{GM} a^2

{4π^2}/{GM} =1

T = in year
a = radius in A.U.
∴ T = 3 days =

3/365

year
∴

a =(3/365)^{2/3}

a = 0.04 A.U.

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