Question:

The correct graph representing the variation of total energy $(E_T)$, kinetic energy $(E_K)$ and potential energy $(E_p)$ of a satellite with its distance $(r)$ from the centre of earth is

Updated On: Jul 5, 2022
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The Correct Option is D

Solution and Explanation

$E_{T}=-\frac{GM\,m}{2r};$ Thus $E_{T}$ increases with increase in $r$ $E_{k}=\frac{GM\,m}{2r}$ ; Thus $E_{k}$ decreases with increase in $r$ $E_{p}=\frac{-GM \,m}{r}$ ; Thus $E_{p}$ increases with increase in $r$
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Concepts Used:

Gravitational Potential Energy

The work which a body needs to do, against the force of gravity, in order to bring that body into a particular space is called Gravitational potential energy. The stored is the result of the gravitational attraction of the Earth for the object. The GPE of the massive ball of a demolition machine depends on two variables - the mass of the ball and the height to which it is raised. There is a direct relation between GPE and the mass of an object. More massive objects have greater GPE. Also, there is a direct relation between GPE and the height of an object. The higher that an object is elevated, the greater the GPE. The relationship is expressed in the following manner:

PEgrav = mass x g x height

PEgrav = m x g x h

Where,

m is the mass of the object,

h is the height of the object

g is the gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity.