what is the gravitational potential energy at the centre of the earth??? If infinity is taken as the reference (i.e zero energy level)
To calculate the gravitational potential energy at the center of the Earth, we need to consider the equation for gravitational potential energy:
Gravitational potential energy (U) = -GMm/r
In this equation, G is the gravitational constant, M is the mass of the Earth, m is the mass of the object experiencing the gravitational force, and r is the distance between the center of the Earth and the object.
As you mentioned, if infinity is taken as the reference point where the gravitational potential energy is considered zero, it means that U is zero when r is infinity. Hence, we have:
0 = -GMm/∞
To determine the gravitational potential energy at the center of the Earth, we need to find the limit as r approaches zero. In this case, as r approaches zero, the value of -GMm/r approaches negative infinity. Therefore, the gravitational potential energy at the center of the Earth, when considering infinity as the reference, is negative infinity.