The ratio of the radius of the Earth to that of the Moon is $10$. The ratio of acceleration due to gravity on the Earth and on the Moon is $6$. The ratio of the escape velocity from the Earth's surface to that from the Moon is

$A$ body of mass $m$ is thrown vertically upward with speed $\sqrt{3} v_e$, where $v_e$ is the escape velocity of a body from the Earth's surface. The final velocity of the body is

The escape velocity of a body on a planet $A$ is $12 \, km/s$. The escape velocity of the body on another planet $B$,whose density is four times and radius is half of the planet $A$,is ................... $km/s$.

Given below are two statements:
Statement $I:$ For a planet,if the ratio of mass of the planet to its radius increases,the escape velocity from the planet also increases.
Statement $II:$ Escape velocity is independent of the radius of the planet.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ body is projected vertically upward from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth,the maximum height attained by the body is:

The potential energy of a satellite is $-8 \times 10^9 \ J$. What is its binding energy (escape energy)?