Question

Moment of Inertia and prove it.
(अथवा)
(OR)
ऊर्जा संरक्षण का नियम लिखिए। सिद्ध कीजिए कि मुक्त रूप से गिरते हुए पिण्ड की कुल यांत्रिक ऊर्जा सदैव
संरक्षित रहती है।
Write Law of Conservation of Energy. Prove that total mechanical energy is
conserved for freely falling body.
312​

Answer 1

Write law of conservation of energy. prove that total mechanical energy is conserved for freely falling body.

solution : law of conservation of energy : according to this theory, total energy is neither created nor destroyed. in short, initial total energy equals to final total energy.

i.e., $T.E_i=T.E_f$

let a body of mass m is dropped from the top of tower of height h.

at height point, velocity of body, u = 0

kinetic energy = 0

potential energy = mgh

so, initial total energy = 0 + mgh = mgh ......(1)

velocity of body before reaching the ground, v = √(2gh)

so, kinetic energy = 1/2 mv² = 1/2 m(2gh) = mgh

potential energy = 0

so final kinetic energy = mgh + 0 = mgh ......(2)

from equations (1) and (2) we get,

initial total energy = final total energy

Therefore it is clear that total mechanical energy (kinetic energy + potential energy) is conserved for freely falling body.