Question:
A spherically symmetric gravitational system of particles has a mass density
$ \rho = \begin{cases}
\rho_0 & \text{for} \; r \le R \\
0 & \text{for} \; r > R
\end{cases}$
where $r_0$ 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 < \infty) $ from the centre of the system is represented by
A spherically symmetric gravitational system of particles has a mass density
$ \rho = \begin{cases}
\rho_0 & \text{for} \; r \le R \\
0 & \text{for} \; r > R
\end{cases}$
where $r_0$ 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 < \infty) $ from the centre of the system is represented by
Updated On: Jan 30, 2025
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The Correct Option is D
Solution and Explanation
Answer (d)
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Concepts Used:
Center of Mass
The center of mass of a body or system of a particle is defined as a point where the whole of the mass of the body or all the masses of a set of particles appeared to be concentrated.
The formula for the Centre of Mass:
Center of Gravity
The imaginary point through which on an object or a system, the force of Gravity is acted upon is known as the Centre of Gravity of that system. Usually, it is assumed while doing mechanical problems that the gravitational field is uniform which means that the Centre of Gravity and the Centre of Mass is at the same position.