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NEET
Exam
NEET
Subject
Physics
Chapter
Mechanical Properties of Fluids

NEET · Physics · Mechanical Properties of Fluids

A vessel in the shape of a truncated cone, which is narrower at the...

A vessel in the shape of a truncated cone, which is narrower at the top and wider at the base, has a base area AA. It is filled with a liquid of density ρ\rho up to a height hh. If the total mass of the liquid in the vessel is MM, how does the force FF exerted by the liquid on the base of the vessel compare to the true weight of the liquid MgMg?

Options

  1. AF=MgF = Mg
  2. BF<MgF < Mg
  3. CF=Mg2F = \dfrac{Mg}{2}
  4. DF>MgF > Mg

Correct answer

D. F>MgF > Mg

Step-by-step solution

The pressure PP exerted by the liquid on the base of the vessel is given by P=ρghP = \rho g h.

The force FF exerted by the liquid on the base is F=P×A=ρghAF = P \times A = \rho g h A.

Because the vessel is narrower at the top and wider at the base, its actual volume VV is less than the volume of a cylinder with the same base area AA and height hh (i.e., V<AhV < A h).

The total mass of the liquid is M=ρVM = \rho V.

Since V<AhV < A h, it follows that M<ρAhM < \rho A h, and the true weight of the liquid is Mg<ρghAMg < \rho g h A.

Therefore, the force exerted on the base is greater than the true weight of the liquid (F>MgF > Mg). This is a classic example of the hydrostatic paradox.

Answer: F>MgF > Mg
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