KVPY SX SB Exam 2018 Question Paper

Question : 98 of 120

Marks: +1, -0

A spiral galaxy can be approximated as an infinitesimally thin disk of a uniform surface mass density (mass per unit area) located at z = 0. Two stars A and B start from rest from heights

2z_0

and

z_0 (z_0

< < radial extent of the disk), respectively, and fall towards the disk, cross over to the other side, and execute periodic oscillations. The ratio of time periods of A and B is

2 $^{–1\/2}$
2
1
2 $^{1\/2}$

Validate

Solution:

Assuming spiral galaxy as a large sheet, then accelration of star is constant

a = c

v ∝ t

z ∝ t^2

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