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I'm really confused how to chose height when calculating potential energy. If an object is right above a desk, suppose the will we take height from desk?

If we take it from a height $x$ from the desk and the level of desk is $y$ from the ground and we change the position of the object such that now the object is directly above the floor. So will the potential energy change as height changes and if so, we know that potential energy is stored energy.

Will the stored energy increase?

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Potential energy stored in a body is relative. We have to first choose the potential at a finite point or infinity. In the case given above, we take potential energy to be 0 at the centre of the Earth. So according to the relation, $PE = mgh$ where $h$ is the height from the centre of the Earth. Generally, we take height from the surface of the Earth and take $9.8 m/s^2$ as the acceleration due to gravity (the $g$ at the surface). Therefore, in your case Potential energy will be $PE = mg(x+y)$.
And since height is directly proportional to the potential energy, as height increases, potential energy increases.

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  • $\begingroup$ So is it that the height is (r+ h ) where r is the radius of earth and h is the height of object from ground level. $\endgroup$ – Abhinav Dhawan Jul 24 '16 at 9:14
  • $\begingroup$ Because you said the h is calculated from center of earth and taking earth spherical height should be (r+ h).But while solving problem height is taken h not r+ h ? $\endgroup$ – Abhinav Dhawan Jul 24 '16 at 9:16
  • $\begingroup$ I said potential energy is relative quantity. If you're calculating it relative to the centre of the Earth then you take height as (r+h). If you're calculating it with respect to the surface, then take height above the surface. $\endgroup$ – Shuvam Shah Jul 24 '16 at 9:18
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    $\begingroup$ Correct. There is no absolute value of potential energy. It can be positive or negative, and where you put the zero point is largely a matter of convenience. Only changes in potential energy matter. $\endgroup$ – PhillS Jul 24 '16 at 9:29
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    $\begingroup$ Potential Energy is not stored in the body, it is the property of the system. $\endgroup$ – Oswald Jul 24 '16 at 10:24

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