Verified Solution • 2025–26 Session moderate

QJEEAdv08Ph5e10: JEE Advanced 2008 Physics - Class 11 JEEAdv08Ph5e10 Solution: A spherically symmetric gravitational system of particles has a …

A spherically symmetric gravitational system of particles has a mass density

ρ={ρ0forr≤R0forr>R

Where ρ0 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

Multiple Choice Options

  • A https://ik.imagekit.io/novatra/photos/3e7e13568f3a1fb788a10c49776185a29d298617e8b57e7cd336c4acbefa2436.webp
  • B https://ik.imagekit.io/novatra/photos/4be86d09c1f8e9ecd47b0c1f2265c00f0d6c53530fc3d285db16015d10fa264d.webp
  • C https://ik.imagekit.io/novatra/photos/11530bd591aa982ed9c63e66d2b3bc3d36bb49e43430ef6ff44bbb10430bb53f.webp
  • D https://ik.imagekit.io/novatra/photos/656c90b64a8ed99ab8c8806b19c79a60aba560b886dda4f8787139a00b1c8e45.webp

Step-by-Step Verified Solution

For r≥R,

Force on test mass m is F=m×|Eg|

where, Eg = Gravitational field intensity at the point of observation

∴ mv2r=m×[GMr2],

Where, M = Total mass of spherical system

∴ v∝1r

For r<R,

F′=m|Eg′|

∴ mV2r=m[GMR3×r]

Hence, V∝r

Related Learning Resources & Exam Preparation