A cubical block of wooden edge l and a density ρfloats in water of density 2 ρ. The lower surfac

step 1 the given data of this question is as there is a cubical block of wood of edge l edge that is l

A cubical block of wooden edge l and a density ρfloats in...

A cubical block of wooden edge $l$ and a density $\rho$ floats in water of density $2 \rho$. The lower surface of eube just touches the free end of a massless spring of force constant $k$ fixed at the bottom of the vessel. The weight $w$ put over the block so that it is completely immersed in water without wetting the weight is (a) $a(l \rho g+k)$ (b) $a(f \rho g+k)$ (c) $a\left(\frac{l \rho g}{2}+2 k\right)$ (d) $l\left(F_{p g}+\frac{k}{2}\right)$

A cubical block of wooden edge $l$ and a density $\rho$ floats in water of density $2 \rho$. The lower surface of eube just touches the free end of a massless spring of force constant $k$ fixed at the bottom of the vessel. The weight $w$ put over the block so that it is completely immersed in water without wetting the weight is
(a) $a(l \rho g+k)$
(b) $a(f \rho g+k)$
(c) $a\left(\frac{l \rho g}{2}+2 k\right)$
(d) $l\left(F_{p g}+\frac{k}{2}\right)$

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Key Concepts

Archimedes' Principle

This principle states that any object fully or partially immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid that is displaced by the object. It is fundamental in determining the floating or sinking conditions of objects in a fluid.

Buoyant Force Calculation

Calculating the buoyant force involves determining the volume of fluid displaced by the object and multiplying it by the density of the fluid and the acceleration due to gravity. This concept is essential in analyzing the equilibrium of floating bodies.

Hooke's Law and Spring Force

Hooke's Law asserts that the force exerted by a spring is proportional to its displacement from equilibrium, characterized by the spring constant. This concept is used to understand how the spring force contributes to the overall force balance on the immersed object.

Equilibrium of Forces

For a system in equilibrium, the total upward force must equal the total downward force. In the context of the problem, the forces include the buoyant force, the gravitational weight, and the restoring force from the spring, all of which must be considered to determine the conditions for complete immersion.

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