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Exam
NEET
Subject
Physics
Chapter
Gravitation

NEET · Physics · Gravitation

A spherically symmetric gravitational system of particles has a...

A spherically symmetric gravitational system of particles has a mass density \rho=\left\{\begin{array}{l} \rho_0 \text{ for } r \leq R \\ 0 \text{ for } r>R \end{array}\right. where ρ0\rho_0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed vv as a function of distance r(0<r<∞)r(0 < r < \infty) from the centre of the system is represented byA spherically symmetric gravitational system of particles has a mass density =\ array l _0 for r ≤ R 0 for r>R array .A spherically symmetric gravitational system of particles has a mass density =\ array l _0 for r ≤ R 0 for r>R array .A spherically symmetric gravitational system of particles has a mass density =\ array l _0 for r ≤ R 0 for r>R array .A spherically symmetric gravitational system of particles has a mass density =\ array l _0 for r ≤ R 0 for r>R array .

Options

  1. AA particle travels along a straight line with a uniform velocity. Its angular momentum
  2. BA particle travels along a straight line with a uniform velocity. Its angular momentum
  3. CA particle travels along a straight line with a uniform velocity. Its angular momentum
  4. DA particle travels along a straight line with a uniform velocity. Its angular momentum

Correct answer

C. A particle travels along a straight line with a uniform velocity. Its angular momentum

Step-by-step solution

For r≤Rr \leq R : mv2r=G⋅mm′r2\frac{m v^2}{r}=\frac{G \cdot m m^{\prime}}{r^2}Here, m′=(43πr3)ρ0m^{\prime}=\left(\frac{4}{3} \pi r^3\right) \rho_0 Substituting in Eq. (i) we get, v∝rv \propto r i.e., v−rv-r graph is a straight line passing through origin. For r>Rr\gt R : mv2r=G⋅m(43πR3)ρ0r2\frac{m v^2}{r}=\frac{G \cdot m\left(\frac{4}{3} \pi R^3\right) \rho_0}{r^2}or V∝1r\quad V \propto \frac{1}{\sqrt{r}} The corresponding v−rv-r graph will be as shown in option (c). ∴\therefore correct option is (c).
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