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MechanicsMedium JEE physics MCQ

Consider a spherical gaseous cloud of mass density $\rho(r)$ in free space where $r$ is the radial distance from its center. The gaseous cloud is made of particles of equal mass $m$ moving in circular orbits about the common center with the same kinetic energy $K$. The force acting on the particles is their mutual gravitational force. If $\rho(r)$ is constant in time, the particle number density $n(r)=\rho(r) / m$ is [ $G$ is universal gravitational constant]
  1. A. $\frac{K}{2 \pi r^{2} m^{2} G}$
  2. B. $\frac{K}{\pi r^{2} m^{2} G}$
  3. C. $\frac{3 K}{\pi r^{2} m^{2} G}$
  4. D. $\frac{K}{6 \pi r^{2} m^{2} G}$

Solution

The correct option is **A**.

PHYSICS

mediumPYQ Reworded
Question
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Consider a spherical gaseous cloud of mass density ρ(r)\rho(r) in free space where rr is the radial distance from its center. The gaseous cloud is made of particles of equal mass mm moving in circular orbits about the common center with the same kinetic energy KK. The force acting on the particles is their mutual gravitational force. If ρ(r)\rho(r) is constant in time, the particle number density n(r)=ρ(r)/mn(r)=\rho(r) / m is [ GG is universal gravitational constant]
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Mechanics — Medium JEE Physics MCQ | MyGoalPrep