Question

The mass density of a spherical body is given by $\rho (r)=\frac{k}{r}$ for $r\le R$ 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 :

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

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