question_answer

Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of r from the centre is proportional to     JEE Main Online Paper (Held On 12 May 2012)

A) r             

B)                        \[{{r}^{-1}}\]

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

D)                        \[{{r}^{-2}}\]

Correct Answer: A

Solution :

                Acceleration due to gravity at depth d from the surface of the earth or at a distance r from the centre 'CV of the earth \[g'=\frac{4}{3}\pi \rho Gr\] Hence \[g'\propto r\]