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A cylindrical vessel is filled upto a height h with a liquid of density p . The cross sectional area of the vessel is A . From the orifice near the bottom, if liquid flows out so that the level falls of h/2 , the work done by gravity in doing so is?
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A cylindrical vessel is filled upto a height h with a liquid of densit...
Problem: Find the work done by gravity when liquid flows out of a cylindrical vessel of height h and cross-sectional area A from the orifice near the bottom, causing the level to fall by h/2.
Solution:
Therefore, the work done by gravity when liquid flows out of a cylindrical vessel of height h and cross-sectional area A from the orifice near the bottom, causing the level to fall by h/2, is (1/4)pAg(h^2).
Solution:
- Initial state: The vessel is filled with liquid up to a height h.
- Final state: The level of the liquid has fallen by h/2.
- Assumptions: The liquid is incompressible and the orifice is small enough to cause a negligible change in the pressure at the bottom of the vessel.
- Work done by gravity: The work done by gravity is equal to the change in potential energy of the liquid.
- Change in potential energy: The initial potential energy of the liquid is mgh, where m is the mass of the liquid, g is the acceleration due to gravity, and h is the initial height of the liquid. The final potential energy of the liquid is (m/2)g(h/2), where (m/2) is the mass of the liquid that has flowed out and (h/2) is the final height of the liquid.
- Work done by gravity: The work done by gravity is given by the difference in potential energy, which is W = mgh - (m/2)g(h/2) = (1/2)mgh.
- Mass of the liquid: The mass of the liquid that has flowed out is given by the product of the density, cross-sectional area, and the height by which the level has fallen, which is (pA(h/2)).
- Final expression: Substituting the mass of the liquid in the expression for work done by gravity, we get W = (1/2)(pA(h/2))(gh) = (1/4)pAg(h^2).
Therefore, the work done by gravity when liquid flows out of a cylindrical vessel of height h and cross-sectional area A from the orifice near the bottom, causing the level to fall by h/2, is (1/4)pAg(h^2).
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A cylindrical vessel is filled upto a height h with a liquid of density p . The cross sectional area of the vessel is A . From the orifice near the bottom, if liquid flows out so that the level falls of h/2 , the work done by gravity in doing so is?
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A cylindrical vessel is filled upto a height h with a liquid of density p . The cross sectional area of the vessel is A . From the orifice near the bottom, if liquid flows out so that the level falls of h/2 , the work done by gravity in doing so is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A cylindrical vessel is filled upto a height h with a liquid of density p . The cross sectional area of the vessel is A . From the orifice near the bottom, if liquid flows out so that the level falls of h/2 , the work done by gravity in doing so is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical vessel is filled upto a height h with a liquid of density p . The cross sectional area of the vessel is A . From the orifice near the bottom, if liquid flows out so that the level falls of h/2 , the work done by gravity in doing so is?.
A cylindrical vessel is filled upto a height h with a liquid of density p . The cross sectional area of the vessel is A . From the orifice near the bottom, if liquid flows out so that the level falls of h/2 , the work done by gravity in doing so is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A cylindrical vessel is filled upto a height h with a liquid of density p . The cross sectional area of the vessel is A . From the orifice near the bottom, if liquid flows out so that the level falls of h/2 , the work done by gravity in doing so is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical vessel is filled upto a height h with a liquid of density p . The cross sectional area of the vessel is A . From the orifice near the bottom, if liquid flows out so that the level falls of h/2 , the work done by gravity in doing so is?.
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