1. Tardigrade
  2. Question
  3. Physics
  4. The mass density of a spherical body is given by ρ (r) = (k/r) for r ≤ R and ρ (r) = 0 for r > R , where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :

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Q. The mass density of a spherical body is given by $\rho (r) = \frac{k}{r}$ for $r \leq R$ and $\rho (r) = 0$ for $r > R$ , where $r$ is the distance from the centre.
The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of $r$ is :

JEE MainJEE Main 2017Gravitation

Solution:

$\rho(r)=\frac{k}{r} \quad r \leq R, \rho(r)=0 \quad r>R$
$g=\frac{G \times \frac{4}{3} \pi r^{3} \times \frac{k}{r}}{r^{2}}, r \leq R$
$=\frac{4 G \pi k}{3}=$ const And
$g=\frac{G \frac{4}{3} \pi R^{3}}{r^{2}}=\frac{4 G \pi R^{3}}{3} \times \frac{1}{r^{2}}$ for $r>R$