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Consider a spherical gaseous cloud of ma...

Consider a spherical gaseous cloud of mass density `rho(r)` in a free space where r is the radial distance from its centre. The gaseous cloud is made of particle of equal mass m moving in circular orbits about their common centre with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If `rho(r)` is constant with time. the particle number density n(r)=`rho(r)` /m is : (g =universal gravitational constant)

A

`(K)/(pi r^(2) m^(2) G)`

B

`(K)/(6pi r^(2) m^(2) G)`

C

`(3K)/(pi r^(2) m^(2) G)`

D

`(K)/(2pi r^(2) m^(2) G)`

Text Solution

Verified by Experts

The correct Answer is:
D
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