Question

A satellite has kinetic energy K, potential energy V and total energy E. Which of the following statements is true?
A. $K = - V/2$
B. $K = V/2$
C. $E = K/2$
D. $E = - K/2$

Answer 1

Hint:The given problem is from gravitational effect between two masses. The total energy of two mass systems due to gravitation depends on masses of both objects and distance between them. The Kinetic energy and potential energy also depends on these parameters. So here we use this approach to solve a given problem.

Complete step by step answer:
As we know that for the earth and satellite system,
Kinetic energy, $K = \dfrac{{GMm}}{{2a}}$
Potential energy, $V = - \dfrac{{GMm}}{a}$
And Total energy, $E = - \dfrac{{GMm}}{{2a}}$
The total energy is summation of kinetic energy and potential energy.
Here G= Gravitational constant
M= Mass of earth
m= Mass of satellite
a= Radius of the orbit of the satellite
On the basis of above three expressions for the energies, we can write that
$K = \dfrac{{GMm}}{{2a}} = - \left( { - \dfrac{{\dfrac{{GMm}}{a}}}{2}} \right) = - \dfrac{V}{2}$

So from the given options, option (A) is the correct choice.
The gravitational potential energy is the energy possessed or acquired by an object due to a change in its position when it is present in a gravitational field. Under the action of gravitational force, the work done is independent of the path taken for a change in position so the gravitational force is a conservative force.
The amount of work done in moving a unit test mass from infinity into the gravitational influence of source mass is known as gravitational potential.
The total energy is defined as the sum of gravitational potential energy and kinetic energy.

Note:Sometimes we ignore the sign of total energy. We should always remember that the total energy due to gravitation is negative but equal in magnitude to the kinetic energy. The kinetic energy is half of potential energy in magnitude.