The escape velocity from a planet is $V_e.$  A tunnel is dug along the diameter of the planet and a small body dropped into it. The speed of the body at the centre of the planet will be

The escape velocity for a body projected vertically upwards from the surface of earth is $11\, km/s$. If the body is projected at an angle of $45^o$ with the vertical, the escape velocity will be ........... $km/s$

The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively ${\rho _1}$ and ${\rho _2}$. The ratio of the accelerations due to gravity at their surfaces is

A body of mass $m$ is lifted up from the surface of the earth to a height three times the radius of the earth. The change in potential energy of the body is

where $g$ is acceleration due to gravity at the surface of earth.

The escape velocity of a body from earth's surface is $v_e$ . The escape velocity of the same body from a height equal to $R$ from the earth's surface will be

Starting from the centre of the earth having radius $R,$ the variation of $g$ (acceleration due to gravity) is shown by