A spherically symmetric gravitational systom of particles has mass density ρ = ρ 0 for r ≤ R 0 for r R where, ρ 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 distance r ( 0 r ∞ ) from the centre of the system is represented by

Question

A spherically symmetric gravitational systom of particles has mass density ρ = ρ 0 for r ≤ R 0 for r > R where, ρ 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 distance r ( 0 r ∞ ) from the centre of the system is represented by, , , ,

MARKS App · Accepted Answer

When r ≤ R , then force on the test mass n at the surface of the sphere = m g Force on the test mass at distance r from the centre of sphere is If r R , then F = G M m R 2 · r R = G M m R 3 · r ∴ m v 2 r = G M m R 3 · r ∴ v α r If r > R then F = G M m r 2 ∴ M v 2 r = G M m r 2 ∴ v α 1 r

Search any question & find its solution

Looking for more such questions to practice?