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A body of mass 50 kg climbs up a rope suspended from the ceiling of a gymnasium.The rope length is 15m.If the body has fallen one third of the way from the

ceiling to the floor, his kinetic energy apporximately


One third from the celling of the floor = 15*1/3 = 5meter
total mechanical energy of the system is conserved 
loss in potential energy = gain in kinetic energy
gain in kinetic energy (K.E.) = m*g*h
m = 50kg
g = 9.8 m/s²
h = 5m
K.E. = 50*9.8*5 = 2450 joule
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Let us assume that the boy has fallen freely, without any friction (without holding the rope tightly) during 15/3 = 5 meters. He was at rest (speed = 0) at the ceiling of the gymnasium. let his mass be m = 50 kg.

The potential energy corresponding to the drop of 5 meters is converted in to the kinetic energy, due to conservation of (mechanical) energy.

Drop in P.E. = m * g * 5 = gain in kinetic energy = KE - 0
So K.E. = 50 * 9.81 * 5 = 2452.5 Joules    (it is 2,500 J if g = 10 m/sec²)

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