Gravitation NCERT Solutions Class 11 Physics - Solved Exercise Question 8.5

Question 8.5:
Let us assume that our galaxy consists of 2.5 × 1011 stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 105 ly.
Solution:
Mass of our galaxy Milky Way, M = 2.5 × 1011 solar mass
Solar mass = Mass of Sun = 2.0 × 1036 kg
Mass of our galaxy, M = 2.5 × 1011 × 2 × 1036 = 5 ×1041 kg
Diameter of Milky Way, d = 105 ly
Radius of Milky Way, r = 5 × 104 ly
1 ly = 9.46 × 1015 m
r = 5 × 104 × 9.46 × 1015
= 4.73 ×1020 m
Since a star revolves around the galactic centre of the Milky Way, its time period is given by the relation:
T = ( 4π2r3 / GM)1/2
= [ (4 X 3.142 X 4.733 X 1060/ (6.67 X 10-11 X 5 X 1041) ]1/2
=   (39.48 X 105.82 X 1030 / 33.35 )1/2
= 1.12 X 1016 s
1 year = 365 X 324 X 60 X 60 s
1s = 1 / (365 X 324 X 60 X 60)  years
∴ 1.12 X 1016 s = 1.12 X 1016 / (365 X 24 X 60 X 60)  =  3.55 X 108 years

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