Multiple choice

Some liquid is filled in a cylindrical vessel of radius $R$. Let ${ F }{ 1 }$ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square cross-section of side $R$. Let ${ F }{ 2 }$ be the force applied by the liquid on the bottom of this new vessel. (Neglect atmosphere pressure). Then

  1. ${ F }_{ 1 }=\pi { F }_{ 2 }$
  2. ${ F }_{ 1 }=\cfrac { { F }_{ 2 } }{ \pi } $
  3. ${ F }_{ 1 }=\sqrt { \pi { F }_{ 2 }}$
  4. ${ F }_{ 1 }={ F }_{ 2 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The force applied by the liquid on the bottom of a vessel is equal to the weight of the liquid column above it (Pressure * Area = Density * g * Height * Area). Since the volume and density are the same, the weight of the liquid is the same in both vessels, resulting in the same force on the bottom.

AI explanation

The force exerted by a liquid on the bottom of a vessel depends solely on the hydrostatic pressure and the base area, which mathematically equates to the total weight of the liquid. Since the exact same liquid is poured into the new vessel, its total mass and the gravitational pull on it remain unchanged regardless of the vessel's shape. Therefore, the force applied to the bottom remains the same in both scenarios.

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