The total mechanical energy of a ball dropped from a tower of height h is the sum of its potential energy and kinetic energy.

Potential Energy:
When the ball is at the top of the tower, it has potential energy due to its position in the gravitational field. The potential energy of an object is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height of the object above a reference point. In this case, the reference point is the ground level.

Kinetic Energy:
As the ball falls from the tower, its potential energy is converted into kinetic energy. Kinetic energy is the energy of an object due to its motion and is given by the equation KE = 0.5mv², where m is the mass of the object and v is its velocity.

Total Mechanical Energy:
The total mechanical energy of the ball is the sum of its potential energy and kinetic energy. Initially, when the ball is at the top of the tower, it has no kinetic energy but only potential energy. As the ball falls, its potential energy decreases while its kinetic energy increases. At the instant the ball hits the ground, all of its potential energy is converted into kinetic energy. Therefore, the total mechanical energy of the ball is the sum of its potential and kinetic energies at any point during its fall.

In this case, the height of the tower is given as h. The potential energy of the ball at the top of the tower is mgh, where m is the mass of the ball. As the ball falls, its potential energy decreases and its kinetic energy increases. At any point during its fall, the sum of its potential and kinetic energies is mgh + 0.5mv².

Therefore, the correct answer is option 'D' - the total mechanical energy of the ball dropped from a tower of height h is the sum of its potential and kinetic energies.