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

Options

A.
B.
C.
D.

Answer

C

Explanation

For `rleR, (mv^(2))/r=(GmM)/(r^(2))to(1)`
here, `M=(4/3pir^(3))rho_(0)`substituting in Eq (1) we get `vpropr` i.e., `v-r` graph is a straight line passing through origin, For `rgtR`
`(mv^(2))/r=(Gm(3/4piR^(3))rho_(0))/(r^(2))` or `vprop1/r`
The corresponding `v-r` graph will be as shown in option (3)