Question

If the gravitational potential at the surface of earth is v, what will be its value at height from surface equal to its radius?

Answer 1

Hint: Gravitational potential is work done per unit mass. Raised weight, water that is behind the dam, ripe fruits before it falls are few examples of gravitational potential. In this question we will use Newton law of universal gravitation which is a product of gravitation and masses divided by radius.

Complete answer:
Gravitation is the natural phenomena which attracts one another having mass or energy and is the weakest force in nature. Law of gravitation gives the gravitational force between any two bodies having the same mass. And this law of gravitation is given by NEWTON. The reason for ocean tides is the moon's gravity .Range of gravity is infinite, and it becomes weaker when the range increases. Examples of gravity are a ball which we throw up in the air with force and come down naturally is because of gravitation, glass that fall on the floor the force that acts on it is called gravitational force, the force that allows moon to revolve around the sun is gravitational force, the force that keeps earth and all the planet in proper position of orbits around the sun is the gravitational force. Gravity has the same effect on each and every object ,if you drop a heavy thing or lighter thing it has the same effect on both .If you drop a feather or elephant in a vacuum when there is no air resistance the amount of force acted is the same . The launch of space vehicles and research development results in great enhancement in measurement of gravity around earth.
Newton discovered the relationship between the moon's motion and the motion of the body which falls freely on earth. Gravitational field is zero at the centre of earth. Formula of universal gravitation at surface is:
\[\begin{align}
  & v=\dfrac{Gm}{r}....Equation1 \\
 & where, \\
 & G=Gravitational Cons\tan t \\
 & m=objectmass \\
 & r=radius \\
 & \\
\end{align}\]
At a particular height \[h=R\]
\[r=R+h=R+R=2R\]
\[\begin{align}
  & {{v}^{1}}=\dfrac{Gm}{r}=\dfrac{Gm}{2R} \\
 & {{v}^{1}}=\dfrac{1}{2}\left( \dfrac{Gm}{R} \right) \\
\end{align}\]
\[{{v}^{1}}=\dfrac{v}{2}\]
Value at which height from surface equal to its radius is \[{{v}^{1}}=\dfrac{v}{2}\].

Note: If you drop a feather or elephant in a vacuum when there is no air resistance, the amount of force acted is the same. The force that holds the gases in the sun is because of gravitational force and the force that causes the apple to fall downward from an apple tree. The force that keeps us walking on earth is called gravitational force.