CBSE Class 11-science Answered
Two cylinders of equal cross sectional area A contain water up to heights h1 and h2. The vessels in them are interconnected so that levels in them are equal. Calculate the work done by the gravity during the process. The density of water is p
Asked by namratas1 | 29 Aug, 2019, 09:43: PM
Expert Answer
Left side figure shows the two cylinders P and Q are initially disconnected have water levels at h1 and h2 as shown in figure.
Potential energy for cylinder P = (ρAh1)(h1/2)g .........................(1)
(potential energy is calculated in eqn.(1) by considering that whole mass is concentrated at middle of water column).
Potential energy for cylinder Q = (ρAh2)(h2/2)g .........................(2)
Total potential energy = (ρAg) ( h12 + h22 )/2 ...........................(3)
after connecting the cyliders as shown in right side figure, height of column in both cylinders will become h
Since total volume remains same, we have, A h1 + A h2 = 2A h or h = (h1 + h2)/2
Hence total potential energy after connecting the cylinders = 2 (ρAg) (h1 + h2)2 /8 = (ρAg) (h1 + h2)2 /4 ...............................(4)
Change in potential energy is obtained by finding the difference of eqn.(3) and eqn.(4)
change in potential energy = [ (ρAg) ( h12 + h22 )/2 ] - [ (ρAg) ( h1 + h2 )2/4 ] = (ρAg) [ { ( h12 + h22 )/4 } - (h1 h2 )/2 ]
change in potential energy = (1/4) (ρAg) ( h1 - h2 )2 .........................(5)
Change in potential energy given by eqn.(5) is the workdone by gravity
Answered by Thiyagarajan K | 30 Aug, 2019, 01:10: PM
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