Question

when a ball is freely fallen from a given height it bounces to 80%

Answer 1

Let a ball fall from a height h, thenKinetic energy of ball at the time striking the ground= Potential energy of ball at height h
so, K.E=mgh
Kinetic energy of ball due to rebounce will be :
K.Er =P.E of ball at height h1= mgh1
Loss of kinetic energy due to re-bounce=K.E -K.Er
=mgh -mgh1=mg(h-h1)=mg(h-80h/100)=mg(20h/100)= 0.2 x mgh
Fractional loss in K.E in each re-bounce will be :=K.E-K.Er/K.E=0.2 x mgh/mgh=0.2=0.2 x100% =20%
Fraction of its Mechanical energy lost in each rebound is 20%