JEE MAIN - Physics (2017 - 9th April Morning Slot - No. 11)
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 :
$$\rho $$ (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 :
_9th_April_Morning_Slot_en_11_1.png)
_9th_April_Morning_Slot_en_11_2.png)
_9th_April_Morning_Slot_en_11_3.png)
_9th_April_Morning_Slot_en_11_4.png)
Explanation
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).
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