Two circular metal plates of radius 1 m and 2 m are placed horizontally in a liquid at rest at

step 1 The question we are given that two metal plates, two metal plates of radius of radius one meter

Two circular metal plates of radius 1 m and 2 m are placed...

Two circular metal plates of radius $1 \mathrm{~m}$ and $2 \mathrm{~m}$ are placed horizontally in a liquid at rest at the same depth. The ratio of thrusts on them is
(A) $1: 2$
(B) $1: 1$
(C) $1: 4$
(D) $4: 1$

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Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It increases linearly with depth according to the relation p = ?gh, where ? is the fluid density, g is the gravitational acceleration, and h is the depth below the surface. This concept is essential for determining the force exerted on any submerged surface.

Pressure Force on a Submerged Surface

The thrust or force on a submerged surface is determined by integrating the fluid pressure over the surface area. For horizontal surfaces located at a constant depth, the pressure is uniform over the entire area, hence the total force (thrust) is calculated as the product of the uniform pressure and the surface area.

Area Calculation of Circular Surfaces

The area of a circle is calculated using the formula A = ?r², where r is the radius of the circle. This calculation is vital when comparing forces on circular plates of different sizes, as the thrust on each plate is directly proportional to its area.

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