A tunnel is dug along the diameter of the earth. There is a particle of mass m at the centre of the tunnel. Find the minimum velocity given to the particle so the is just reaches to the surface of the earth.

\(\sqrt{\frac{GM}{R}}\) \(\sqrt{\frac{2GM}{R}}\) \(\sqrt{\frac{GM}{2R}}\) it will reach with the help of negligible velocity

\(\sqrt{\frac{GM}{R}}\)

\(\frac{1}{2}mv^2 = -\frac{GMm}{R} + \frac{3GMm}{2R}\) \(\frac{1}{2}mv^2 = \frac{GMm}{2R}\) \(\Rightarrow v = \sqrt{\frac{GM}{R}}\)