Experts please long answer type
questions number 5

Solution : 

5.)
The law of conservation of energy states that energy can neither be created nor it can be destroyed; it can only be transformed from one from to the other.

• Top

Let us consider a ball of mass m falling from rest down from a wall of height h.

Since the ball is in rest the KE = ½mv² = 0, PE = mgh

Total energy = PE + KE = mgh + 0 = mgh.

• In between 

Let us consider an intermediate position of the falling ball at a height x from the ground

PE of the ball at height x from ground = mgx

Now velocity of the ball at that point, applying

v² = u² + 2gs

u = 0, here displacement s = h - x

Thus v² = 2g(h-x)

Now KE = ½mv²

=> KE = ½m×2g(h-x) = mg(h-x)

E = KE + PE = mgx + mg(h-x) = mgh  
 

• At bottom just before hitting the ground 

Here PE = mg×0 = 0

Velocity of the ball v² = 2gh

KE = ½mv² = ½m×2gh = mgh. 

Neglecting air resistance we have seen that in the above cases the total energy remains the same = mgh.

Thus, the total energy is unchanged and initial energy = mgh = final energy. 
Hence, total energy remains constant or conserved.