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 that just reaches to the surface of the earth. (R=radius of earth)

Q. A tunnel is dug along the diameter of the earth(radius R and mass M). There is a particle of mass 'm' at the centre of the tunnel. The minimum velocity given to the particle so that it just reaches to the surface of the earth is?

Q. A tunnel is dug along the diameter of the earth (radius $R$ and mass $M$). There is a particle of mass ${}^{\prime }{m}^{\prime }$ at the centre of the tunnel. Find the minimum velocity given to the particle so that it just reaches to the surface of the earth is

Q. A tunnel is dug along the diameter of Earth.There is a particle of mass $m$ at the centre of tunnel.The maximum velocity given to the particle, so that it just reaches the surface of earth is: $(R$ is radius of Earth and $M$ is the mass of the earth $)$

Q. A smooth and bottomless tunnel is dug through the centre of earth. A particle is released from the surface of earth into the tunnel. Time to reach centre of tunnel is (approximately) equal to (where $R=$ Radius of earth).

Q. A tunnel is dug inside the earth across one of its diameters. Radius of earth is $R$ and its mass is $M$. A particle is projected inside the tunnel with velocity $\sqrt{\frac{2GM}{R}}$ from one of its ends then maximum velocity attained by the particle in the subsequent motion is (assuming tunnel to be frictionless)