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Mechanical Properties Of Fluids

Question
CBSEENPH11020524

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is [Latent heat of ice is 3.4 x 105 J/kg and g =10 N/kg]

  • 544 km

  • 136 km

  • 68 km

  • 34 km

Solution

B.

136 km

As per conservation of energy, energy gained by the ice during its fall from height h is given by,
straight E space equals space mgh
Given, only one-quarter of its energy is absorbed by the ice.
So, 
mgh over 4 space equals space m L subscript f
rightwards double arrow space h space equals space fraction numerator m L subscript f space x space 4 over denominator m g end fraction
space space space space space space space space space space equals space fraction numerator L subscript f x 4 over denominator g end fraction
space space space space space space space space space equals space fraction numerator 3.4 space x space 10 to the power of 5 x 4 over denominator 10 end fraction
space space space space space space space space equals space 13.6 space x space 10 to the power of 4
space space space space space space space space equals space 13600 space m space
space space space space space space space space equals space 136 space k m