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A spherically symmetric gravitational sy...

A spherically symmetric gravitational system of particles has a mass density` rho={(rho_0,for, r,lt,R),(0,for,r,gt,R):}` where`rho_0` is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as a function of distahce `r(0ltrltOO)` form the centre of the system is represented by

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
C
`F=(GMm)/(R^(3))r=(mv^(2))/(r)impliesvpropr,rltR`
`(GMm)/(r^(2))=(mv^(2))/(r)impliesvprop(1)/(sqrt(r)),rgtR`
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