A strength smooth tunnel is dug through a spherical planet and is perpendicular to the planet’s axis of rotation, which is fixed in space. The planet rotates with the angular velocity ω so that objects in the tunnel have no acceleration relative to the tunnel. Find the value of ω.

Q: A strength smooth tunnel is dug through a spherical planet and is perpendicular to the planet’s axis of rotation, which is fixed in space. The planet rotates with the angular velocity ω so that objects in the tunnel have no acceleration relative to the tunnel. Find the value of ω.

(a) $\sqrt{\frac{4}{3}} \pi G \rho_0 $

(b) $\sqrt{\frac{2}{3}} \pi G \rho_0 $

(c) $\sqrt{\frac{1}{3}} \pi G \rho_0 $

(d) $2 \sqrt{\frac{4}{3}} \pi G \rho_0 $

Ans: (a)