question_answer

                                                                  The gravitation field (g) inside the earth is proportional to r as (where, r is distance from the centre)

A)  \[\frac{1}{r}\]                                  

B)  \[\frac{1}{{{r}^{2}}}\]

C)  \[{{r}^{2}}\]                                      

D)  \[r\]

Correct Answer: D

Solution :

 Idea Here, earth is considered as a solid sphere of mass in mass Mg. The intensity of gravitational field is equal to\[\frac{G{{M}_{e}}}{R_{r}^{3}}r\] \[{{g}_{\text{inside}}}=\frac{G{{M}_{e}}r}{R_{e}^{3}}\Rightarrow {{g}_{\text{inside}}}\propto r\] TEST Edge Shell of uniform mass distribution of mass M (i) Force on \[{{m}_{1}}\] due to shell = zero. (ii) Force on \[{{m}_{2}}\] due to shell \[=\frac{GM{{m}_{2}}}{r_{2}^{2}}\]