Moment of Inertia and prove it.
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Write Law of Conservation of Energy. Prove that total mechanical energy is
conserved for freely falling body.
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Answers
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.,
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.