derive the mathematical expression of upward thrust
Answers
Explanation:
1) When a body is partly or totally immersed in a fluid there is an upthrust that is equal to the weight of fluid displaced.
2) Upthrust = apparent loss of weight of object = weight in air - weight in liquid.
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How can we derive the formula of upthrust?
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Upthrust is a kind of force which always acts in upward direction right? And, we know, Force = Pressure × Area. In this case, the pressure is extended on a body by a liquid and hence the pressure will be liquid pressure. Let's see !
Upward force or upthrust exerted on a body by liquid = Pressure exerted om that body by the liquid × Area of cross section (or, the base area of the solid which is immersed in the liquid of density “D”) = height of the base of the solid object from just below the free surface of the liquid (h) × density of the liquid (d) × acceleration due to gravity (g) × Area of cross section of the solid immersed (A) = volume of the solid immersed in that liquid (V) × density of the liquid (d) × acceleration due to gravity (g)
Thus, upthrust which is actually a force, is equal to the product of volume of the solid immersed in that liquid (V) × density of the liquid (d) × acceleration due to gravity (g)
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