The ratio of the escape velocity of a planet to the escape velocity of the Earth will be: Given: Mass of the planet is $16$ times the mass of the Earth and the radius of the planet is $4$ times the radius of the Earth.

The escape velocity for a planet is $v_e$. $A$ tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet,its speed will be

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Earth has an atmosphere,whereas the Moon does not have any atmosphere.
Reason $R$: The escape velocity on the Moon is very small compared to that on the Earth.
In the light of the above statements,choose the correct answer from the options given below:

The value of escape velocity on a certain planet is $2 \, km/s$. Then the value of orbital speed for a satellite orbiting close to its surface is

The escape velocity from the Earth's surface is $v$. The escape velocity from the surface of another planet having a radius four times that of Earth and the same mass density is:

The velocity with which a projectile must be fired so that it escapes Earth's gravitation does not depend on