State the law of conservation of mechanical energy. Show that total mechanical energy of a body falling freely under gravity is conserved.

Explanation

Energy can neither be created nor destroyed but can be transformed into other forms of energy.
Let a particle be at 'C'. Initially the particle will be zero velocity. Let 'h' be the height of the particle.
`P.E_(C)=mgh," "K.E_(C)=0`,
`T.E_(C)` = mgh
At B, `K.E_(B)=1//2mv_(B)`
`=1//2m(2gx)`
= mgx
`P.E_(B)=mg(h-x)`
Hence `T.E_(B)=(mgh-mgx)+(mgx)`
= mgh
At A, `v_(A)^(2)=2gh`
So that `K.E_(A)=(1)/(cancel2)mcancel2gh`
= mgh
`P.E_(A)=0`
Hence at all points. A, B and C, the total energy is conserved.