A conical block floats in water with 90 % height immersed in...

A conical block floats in water with $90 \%$ height immersed in it. Height $h$ of the block is equal to the diameter of the block, i.e., $20 \mathrm{~cm}$. The mass to be kept on the block, so that the block just floats at the surface of water, is (A) $568 \mathrm{~g}$ (B) $980 \mathrm{~g}$ (C) $112 \mathrm{~g}$ (D) $196 \mathrm{~g}$

A conical block floats in water with $90 \%$ height immersed in it. Height $h$ of the block is equal to the diameter of the block, i.e., $20 \mathrm{~cm}$. The mass to be kept on the block, so that the block just floats at the surface of water, is
(A) $568 \mathrm{~g}$
(B) $980 \mathrm{~g}$
(C) $112 \mathrm{~g}$
(D) $196 \mathrm{~g}$

Key Concepts

Volume of a Cone

The volume of a cone is determined by its geometric dimensions and is calculated using the formula V = (1/3)?r²h. Understanding how to compute the volume of a conical solid is crucial in problems involving buoyancy, as it allows one to find the amount of fluid displaced by the submerged portion of the cone when it is partially immersed.

Density and Mass Relationship

The density and mass relationship, expressed by the equation mass = density × volume, is central to connecting the volume of displaced fluid with its weight. In buoyancy problems, knowing the density of the fluid helps in calculating the weight of the fluid displaced, which is then compared to the weight of the floating body to determine its equilibrium state.

Archimedes' Principle

Archimedes' Principle states that any object wholly or partially immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object. This principle is fundamental in analyzing the floating and sinking behavior of bodies in fluids and is key to determining the amount of displaced fluid in equilibrium problems.

Buoyancy Equilibrium

Buoyancy equilibrium occurs when the upward buoyant force acting on a floating body exactly balances the downward gravitational force (weight) acting on it. This equilibrium condition is used to determine the submersion level of the object and can be adjusted by adding extra mass, so that the effective weight equals the weight of the displaced fluid, ensuring the object is just floating.

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