The change in the value of '$g$' at a height '$h$' above the surface of the earth is the same as at a depth '$d$' below the surface of earth. When both '$d$' and '$h$' are much smaller than the radius of earth, then which one of the following is correct ?
- $d=\frac{h}{2}$
- $d=\frac{3h}{2}$
- $d=2\,h$
- $d=h$
The Correct Option is C
Solution and Explanation
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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.