$A$ body is projected vertically upwards with a speed of $\sqrt{\frac{G M}{R}}$ ($M$ is the mass and $R$ is the radius of the Earth). The body will attain a maximum height of .......

What is the minimum energy required to launch a satellite of mass $m$ from the surface of the Earth of mass $M$ and radius $R$ to an altitude of $2R$?

$A$ missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is

Two planets have masses $M$ and $16\, M$ and their radii are $a$ and $2\, a$ respectively. The separation between the centres of the planets is $10\, a.$ $A$ body of mass $m$ is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of the smaller planet,the minimum firing speed needed is

An object is projected vertically upward from the earth's surface with a velocity $u = \sqrt{Rg}$,where $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the earth's surface. Find the maximum height reached by the object.

$A$ body is thrown from the surface of the earth with velocity $V \ m/s$. The maximum height above the earth's surface up to which it will reach is ($R =$ radius of earth,$g =$ acceleration due to gravity).