A solid piece of aluminum (ρ=2.70 g / cm^3) has a mass of...

A solid piece of aluminum $\left(\rho=2.70 \mathrm{~g} / \mathrm{cm}^{3}\right)$ has a mass of $8.35 \mathrm{~g}$ when measured in air. If it is hung from a thread and submerged in a vat of oil $\left(\rho=0.75 \mathrm{~g} / \mathrm{cm}^{3}\right)$, what will be the tension in the thread?

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Key Concepts

Archimedes' Principle

Archimedes' Principle states that an object fully or partially submerged in a fluid experiences an upward force equal to the weight of the fluid it displaces. This principle is fundamental in understanding how buoyancy affects the forces acting on immersed bodies.

Density

Density is defined as the mass of an object per unit volume. It is a critical concept for calculating the volume of a substance when its mass is known, as well as for determining the behavior of materials when interacting with fluids.

Buoyant Force

The buoyant force is the upward force exerted by a fluid on a submerged object, and it is calculated by multiplying the volume of the displaced fluid, the density of the fluid, and the acceleration due to gravity. This force reduces the effective weight of the object in the fluid.

Apparent Weight

Apparent weight is the weight of an object as measured when it is submerged in a fluid. It is lower than the actual weight due to the buoyant force acting in opposition to gravity, which is an important consideration when determining the tension in a supporting thread.

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