$A$ body is thrown from the surface of the earth with velocity $u \ m \ s^{-1}$. The maximum height in meters above the surface of the earth up to which it will reach is ($R=$ radius of the earth,$g=$ acceleration due to gravity).

An object is allowed to fall from a height $R$ above the earth,where $R$ is the radius of the earth. Its velocity when it strikes the earth's surface,ignoring air resistance,will be:

If $g$ is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass $m$ raised from the earth's surface to a height equal to the radius $R$ of the earth is

Work done in raising a body of mass $m$ from the surface of the earth to a height $\frac{R}{3}$ is ......... (where,$R$ is radius of earth,$M$ is mass of the earth and $G$ is gravitational constant)

If a body is projected vertically from the surface of the earth with a speed of $8000 \,ms^{-1}$, then the maximum height reached by the body is (Radius of the earth $= 6400 \,km$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $km$)

Two stars each of one solar mass $\left(=2 \times 10^{30} \; kg\right)$ are approaching each other for a head-on collision. When they are at a distance of $10^{9} \; km$,their speeds are negligible. What is the speed with which they collide? The radius of each star is $10^{4} \; km$. Assume the stars remain undistorted until they collide. (Use $G = 6.67 \times 10^{-11} \; N \cdot m^{2}/kg^{2}$)