If $g$ is the acceleration due to gravity at the earth's surface and $r$ is the radius of the earth,the escape velocity for a body to escape out of the earth's gravitational field is

The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$) to infinity is:

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 masses of two fixed spheres are $M$ and $2M$ and the radius of each sphere is $R$. Their centres are $10R$ apart. The minimum speed with which a particle of mass $\frac{M}{10}$ be projected from the mid-point of the line joining the centres of the two spheres so that it escapes to infinity is . . . . . . .

Escape velocity of a body of $1\, kg$ mass on a planet is $100\, m/s$. Gravitational potential energy of the body on the surface of the planet is ......... $J$.

$A$ planet has twice the radius but the mean density is $\frac{1}{4}^{th}$ as compared to Earth. What is the ratio of the escape velocity from Earth to that from the planet?