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CBSE Class 12-science Answered

A tank of height 5m is completely filled with water. work done to empty a tank to one fourth of its depth such that initial mass of water in tank is 50 kg is.
Asked by sbtech357 | 22 Jul, 2018, 03:50: PM
answered-by-expert Expert Answer
It is assumed the tank has to be emptied to 1/4 th of its height oer upto 1.25 m from its bottom as shown in figure.
 
Workdon to empty the volume of water above mentioned is same as loss of potential energy.
 
let us consider a small slice of water element of thickness dh at a height h as shown in figure.
 
potential energy dE of this water element is given by,  dE = dm×g×h Joules
 
dm is mass content of this water element,  dm = (M/H)dh, where M is total mass of water in the tank and H is its height, H= 5 m.
 
hence dE = (M/H)×g×h×dh   Joules
 
Then total loss of potential energy begin mathsize 12px style equals space integral subscript 1.25 end subscript superscript 5 open parentheses M over H close parentheses cross times g cross times h cross times d h space equals space open parentheses M over H close parentheses cross times g cross times 1 half cross times open parentheses 25 minus 1.5625 close parentheses space equals open parentheses 50 over 5 close parentheses cross times 9.8 cross times 1 half cross times 23.4375 space equals space 1148 space J end style
Hence the required workdone = 1148 J
Answered by Thiyagarajan K | 22 Jul, 2018, 05:51: PM

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