Home
Class 11
PHYSICS
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
For `rleR,(mv^(2))/r=(GmM)/(r^(2))`
Here `M=(4/3pir^(3))rho_(0)`
Substituting in eqn i we get
`vpropr`
i.e. `v-r` graph is a straight line passing through the origin.
For `rgtR,`
`(mv^(2))/r=(GM(4/3piR^3)rho_(0))/(r^(2))`
`implies vprop1/(sqrt(r))`
The corresponding `v-r` graph will be as shown in option c.
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    CENGAGE PHYSICS|Exercise MCQ_TYPE|4 Videos

  • GRAVITATION

    CENGAGE PHYSICS|Exercise AR_TYPE|1 Videos

  • GRAVITATION

    CENGAGE PHYSICS|Exercise True/False|1 Videos

  • FLUID MECHANICS

    CENGAGE PHYSICS|Exercise INTEGER_TYPE|1 Videos

  • KINEMATICS-1

    CENGAGE PHYSICS|Exercise Integer|9 Videos

Similar Questions

Explore conceptually related problems

Which one of the following plots represents the variation of the gravitational field on a particle with distance r due to a thin spherical shell of raduis R ? ( r is measured from the centre of the spherical shell).

Two particles of equal mass m go around a circle of radius R under the action the of their mutual gravitational attraction . The speed v of each particle is

The density inside a solid sphere of radius a is given by rho=rho_(0)(1-r/a) , where rho_(0) is the density at the surface and r denotes the distance from the centre. Find the gravitational field due to this sphere at a distance 2a from its centre.

Three particles of equal mass M each are moving on a circular path with radius r under their mutual gravitational attraction. The speed of each particle is

A test particle is moving in a circular orbit in the gravitational field produced by a mass density rho(r)=K/r^2 . Identify the correct relation between the radius R of the particle’s orbit and its period T: