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 . It is filled with a liquid of density up to a height . If the total mass of the liquid in the vessel is , how does the force exerted by the liquid on the base of the vessel compare to the true weight of the liquid ?
Options
- A
- B
- C
- D
Correct answer
D.
Step-by-step solution
The pressure exerted by the liquid on the base of the vessel is given by .
The force exerted by the liquid on the base is .
Because the vessel is narrower at the top and wider at the base, its actual volume is less than the volume of a cylinder with the same base area and height (i.e., ).
The total mass of the liquid is .
Since , it follows that , and the true weight of the liquid is .
Therefore, the force exerted on the base is greater than the true weight of the liquid (). This is a classic example of the hydrostatic paradox.
Answer:
The force exerted by the liquid on the base is .
Because the vessel is narrower at the top and wider at the base, its actual volume is less than the volume of a cylinder with the same base area and height (i.e., ).
The total mass of the liquid is .
Since , it follows that , and the true weight of the liquid is .
Therefore, the force exerted on the base is greater than the true weight of the liquid (). This is a classic example of the hydrostatic paradox.
Answer: