See P.E is=mgh. It means at any max height its value would be max. When it freely falls down to crust the value of "h" starts decreasing and the P.E simultaneously decreases. Also due to "0" value of velocity at the max height the value of K.E is "0" . When it falls it attains velocity and the decreased P.E is converted into K.E during fall. This gives rise to conservation of mechanical energy. Yes, the min P.E is present at the min height.

Defining the Minimum Potential Energy of a Dropped Object

When an object is dropped from a certain height, it possesses potential energy due to its position in the Earth's gravitational field. The minimum potential energy of the object can be defined by considering the following factors:

The Concept of Potential Energy:
Potential energy is the energy possessed by an object due to its position or state. In the case of an object dropped from a height, it possesses gravitational potential energy.

Gravitational Potential Energy:
Gravitational potential energy is the potential energy associated with an object's vertical position in a gravitational field. It depends on the object's mass (m), acceleration due to gravity (g), and height (h) from which it is dropped.

The Equation:
The minimum potential energy (PE) of a matter dropped from a height can be calculated using the equation:

PE = m * g * h

Where:
- PE is the potential energy
- m is the mass of the object
- g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
- h is the height from which the object is dropped

Example Calculation:
Let's consider an object with a mass of 2 kg dropped from a height of 10 meters. Using the equation mentioned above, we can calculate the minimum potential energy.

PE = 2 kg * 9.8 m/s² * 10 m
PE = 196 Joules

Therefore, the minimum potential energy of the object when it is dropped from a height of 10 meters is 196 Joules.

Key Points:
- Potential energy is the energy possessed by an object due to its position or state.
- Gravitational potential energy is the potential energy associated with an object's vertical position in a gravitational field.
- The minimum potential energy of a matter dropped from a height can be calculated using the equation PE = m * g * h.
- The mass, acceleration due to gravity, and height are the factors considered in calculating potential energy.
- The unit of potential energy is Joules (J).