# State and prove the law of conservation of energy in the case of a freely falling object.

m = mass of body

g = Acceleration due to gravity

Suppose a body is at point A initially. Then it falls freely, during the motion mechanical energy of the body is conserve.

At point A,

AC = height of object from ground

= h

Initial speed u = 0

So, P.E. = mgh

TE = P.E + K.E = mgh + 0

(TE)_{A }= mgh ... (i)

At point B,

PE = mg (BC)

= mg (h – x) = mgh – mgx

Use kinematics equation

(TE)_{B} = P.E. + K.E = mgh – mgx + mgx

= mgh ...(ii)

At point C,

P.E. = 0

Use kinematics equation

⇒ v ^{2} = 2gh

So,

(T.E.)_{C }= K.E + P.E. = mgh +0 = mgh ...(iii)

(TE)_{A} =(TE)_{B}=(TE)_{C}

Hence, the total energy of the body is conserve during free fall.

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