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500 persons are taking a dip into a cuboidal pond which is 80m long and 50m broad. Find the rise of water level in the pond in millimetres, if the average displacement of water by a person is 0.04m3.

500 persons are taking a dip into a cuboidal pond which is 80m long and 50m broad. Find the rise of water level in the pond in millimetres, if the average displacement of water by a person is 0.04m3.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
10 days ago
Using the average displacement and number of persons we can find the total displacement of water. Then this can be equated with the rise in volume of water in the pond. Using the equation of volume of a cuboid we can calculate the rise in water level. Formula used: Volume of a cuboid, V=lbh, where l,b,h are the length, breadth and height respectively. Average of some value is calculated by dividing the total by its number. Complete step-by-step solution: Given that, Length of the pond, l=80m Breadth of a pond, b=50m Number of persons taken dip, n=500 Average displacement of water by a person is 0.04m3. Average of some value is calculated by dividing the total by its number. Therefore, total displacement of water by 500 persons is equal to 500×0.04=20m3. We can see that the displacement of water is equal to the rise in volume of water in the pond. And this volume will be equal to 80×50×h where h is the change in height occurred by rise in water level. This is because the water level increased is equally distributed to a cuboidal area and volume of a cuboid, V=lbh So we have, ⇒80×50×h=20 This gives ⇒h=2080×50 ⇒h=1200 Thus the rise in water level is 1200m. We know, 1m=1000mm This gives the rise in water level equal to 1200×1000=5mm. ∴ The answer is 5mm. Note: When an object falls into a water body, the level of the water rises. Also this water is equally distributed over the surface whatever the shape of the body. So we can equate it with rise in volume. This is the important point used here.

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