Q: The escape velocity from the surface of the earth of radius R and density ρ ?

(a) $\displaystyle 2R \sqrt{\frac{2 \pi \rho \,G}{3}} $

(b) $ \displaystyle 2 \sqrt{\frac{2 \pi \rho \,G}{3}} $

(c) $ \displaystyle 2\pi \sqrt{\frac{R}{g}} $

(d) $ \displaystyle \sqrt{\frac{2 \pi \rho \,G}{R^2}} $

Ans: (a)