Suppose a vertical tunnel is along the diameter of earth (here earth is assumed to be a sphere of uniform mass density $\rho$). If a body of mass m is thrown in this tunnel, its acceleration at a distance y from the centre is given by

• A

  $\frac{4\pi }{3}\mathit{\text{G}}\text{ρ}\mathit{\text{ym}}$

• B

  $\frac{3}{4}\pi \text{ρ}\mathit{\text{y}}$

• C

  $\frac{4}{3}\pi \text{ρ}\mathit{\text{y}}$

• D

  $\frac{4}{3}\pi G\text{ρ}\mathit{\text{y}}$