A lead ball at 25oC is dropped from a height of 2 km. It is heated due to air resistance and it is assumed that all of its kinetic energy is used in increasing the temperature of ball. If specific heat of lead is s = 125 Joule/kg oC, the final temperature of ball in oC is __________. g=10 m / sec 2
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answer is 160.
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Detailed Solution
If there is no air resistance, velocity of ball on reaching ground isV=2gh=2×10×2000=200m/sKinetic energy of ball is K=12mv2=12×m×(200)2=2×104×m Joule [if mass m is in kg]If all the kinetic energy is absorbed by the ball as heated due to this temperature of ball is increased by ∆T, we have K=msΔTor 2×104×m=m×125×ΔTor ΔT=ΔT=2×104125=160∘C