Question

prove law of coservation of energy​

Answer 1

Law of conservation of energy states that Energy is neither be created or nor destroyed. ...in other words we can say "the total energy of a closed system always remains constant". This law is valid on all situation and for all type of transformation.

Answer 2

Body of mass m placed at a height h
At A,
Potential energy = mgh

Kinetic energy = 0 [the velocity is zero as the object is initially at
rest]
Total energy at A = Potential energy + Kinetic energy.

Total energy at A = mgh …1
At B,
Potential energy = mgh
= mg(h - x) [Height from the ground is (h-x)]
Potential energy = mgh - mgx
Kinetic energy = ½ mv2
The body covers the distance x with a velocity v. We make use of the third equation of motion to obtain velocity of the body.

Here, u=0, a=g and s=x



Kinetic energy = mgx
Total energy at B = Potential energy + Kinetic energy

Total energy at B = mgh …2
At C,
Potential energy = m x g x 0
Potential energy = 0
Kinetic energy = ½ mv2
The freely falling body has covered the distance h.

Here, u=0, a=g and s=h

Kinetic energy = ½ mv2

Kinetic energy = mgh
Total energy at C = Potential energy + Kinetic energy

Total energy at C = mgh …3
It is clear from equations 1, 2 and 3 that the total energy of the body remains constant at every point. Thus, we conclude that law of conservation of energy holds good in the case of a freely falling body.