question_answer

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 -        [JEE Online 09-04-2017]

A)           

B)  

C)         

D)  

Correct Answer: A

Solution :

                \[\frac{M}{V}\,=\frac{k}{r}\] for inside \[M=\frac{kv}{r}\] \[g=\frac{Gmr}{{{R}^{3}}}\,=\frac{G}{{{R}^{3}}}.\,\frac{kv}{r}.\,r=\,\operatorname{constant}\] \[{{g}_{out}}\,=\frac{GM}{{{R}^{2}}}\]