Assume that a tunnel is dug through earth from North pole to south pole and that the earth is a non-rotating, uniform sphere of density $\rho $. The gravitational force on a particle of mass $m$ dropped into the tunnel when it reaches a distance $r$ from the centre of earth is
Assume that a tunnel is dug through earth from North pole to south pole and that the earth is a non-rotating, uniform sphere of density $\rho $. The gravitational force on a particle of mass $m$ dropped into the tunnel when it reaches a distance $r$ from the centre of earth is
- A
$\left( {\frac{3}{{4\pi }}\,mG\rho } \right)r$
- B
$\left( {\frac{{4\pi }}{3}\,mG\rho } \right)r$
- C
$\left( {\frac{{4\pi }}{3}\,mG\rho } \right)r^2$
- D
$\left( {\frac{{4\pi }}{3}\,{m^2}G\rho } \right)r$
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