Question

prove that the total energy at any point in the path of a dropped mass is mg times the height from where it is dropped

Answer 1

Hey there! ☺☻☺

Assume a object of mass m.
And it is raised to height h. 

By this we know that the work is done against the gravity in raising a body to height h. And some force will be required to raise it to height h. As the weight is acting vertically downward so the force = mg and displacement will be height h.

Now we know,
Work = force * displacement
         = mg * h 
         = mgh

Hence, The total energy at any point in the path of a dropped mass is mg * h from where it dropped and is known as Gravitational Potential Energy.

Hope It Helps You! ☺☻☺