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76. Problem 18.23 (RHK) A jug contains 15 glasses of orange juice. When we open the tap at the bottom it takes 12.0 s to full the first glass. We have to find the time taken when tap is kept open for the jug to empty out. |
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Solution: Click For PDF Version Let the cross-section of the jug be A m2. Let
height of juice at time t in the jug when the tap at the bottom of the
jug is open be
From this data the initial height of the level of juice in
the jug is
Also,
Therefore, rate of change of the level of juice in the jug will be
Integrating this equation, we find that
We are given that the first glass is filled in 12 s. That is
Time T for complete draining out of juice from the jug
is given by
We thus find that the time required for filling the remaining 14 glasses after the first glass has been filled will be 342 s or 5 min 42 s. |
. Let the
area of cross-section of the tap, which is at the bottom of the jug, be a
m2. Let the speed of flow of the juice at time t be
.
and the
height when the first glass has been filled will be
.
This gives
that is
