Question 220: Gravitation

Question

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

Accepted Answer

For inside the spherical body, we have
$${m \over v} = {k \over r}$$
$$ \Rightarrow m = {{kv} \over r}$$
Therefore, $$g = {{Gmr} \over {{R^3}}} = {G \over {{R^3}}}\left( {{{kv} \over r}} \right)r$$ = constant
For inside the spherical body, we have
$${g_{out}} = {{GM} \over {{R^2}}}$$
Therefore, the correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is the one depicted in option (c).

Answer

Answer

Answer

Answer

Gravitation

The mass density of a spherical body is given by $\rho (r) = {k \over 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 :

Choose the correct answer: