This chapter presents a more formalized treatment of gravitational potential ene

Question

This chapter presents a more formalized treatment of gravitational potential energy - from a universal perspective. Which of the following is NOT true about gravitational potential energy under this treatment? A) The derivative of gravitational potential energy gives a force which is always attractive. B) Gravitational potential energy is negative everywhere. C) Gravitational potential energy is only zero at a point infinitely far away from the massive object in the problem. D) Gravitational potential energy on Earth's surface (the flat-Earth approximation) will give the value of 9.8 m/s

Explanation / Answer

The minus sign in the gravitational force signifies that the direction of force is always opposite to the displacement or position vector of the body which is kept in the gravitational field of the source body and the same goes with respect to the other body as well.

Hence as we move away from a mass, the force vector's direction is opposite to the direction where we are moving.This is what the negative sign signifies which we also call attractive force.

But when we find the derivative of Gravitational Potential Energy we get only the magnitude of the Gravitational force ( no minus sign) . There fore we cannot say whether its attractive or not ; however we know its always attractive and never repulsive.

Option B is always true

For option C, we can say that the Gravitational Potential Energy is 0 at distance infinity from the source ( by convention)

And Option D , from Gravitational potential energy we cannot calculate the value of g on earth's surface ; we can calculate it from gravitational force. However , we can derive gravitational force by taking derivative of Gravitational Potential Energy.

So, the answer should be D but we should also ponder about the issue raised in option A

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