**Problem Statement:**An aluminum cube of edge length 20 cm floats on mercury. How much extra depth will the cube sink when the temperature rises from 270 K to 320 K?**Explanation:**This problem involves understanding the thermal expansion of materials and buoyancy principles. When the temperature changes, materials expand or contract. The degree to which they change in volume can affect how an object floats due to changes in density and buoyancy.**Concepts to Explore:**- **Thermal Expansion:** How materials expand with temperature. For a cube, the change in volume can be calculated using the coefficient of linear expansion.- **Buoyancy:** How objects float, based on Archimedes' principle. As the cube expands, its density relative to the mercury changes, affecting how much of it is submerged.- **Density Changes:** How the density of the mercury might slightly change with temperature, also affecting buoyancy.By understanding these concepts, one can solve for the additional sinking depth of the cube in the mercury.

Consider at a particular temperature the aluminum cube sinks a depth h and density of mercury is .…

Answered: An aluminum cube of edge length 20 cm…

An aluminum cube of edge length 20 cm floats on mercury. How much extra depth will the cube sink when the temperature rises from 270 K to 320 K?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

**Problem Statement:**

An aluminum cube of edge length 20 cm floats on mercury. How much extra depth will the cube sink when the temperature rises from 270 K to 320 K?

**Explanation:**

This problem involves understanding the thermal expansion of materials and buoyancy principles. When the temperature changes, materials expand or contract. The degree to which they change in volume can affect how an object floats due to changes in density and buoyancy.

**Concepts to Explore:**

- **Thermal Expansion:** How materials expand with temperature. For a cube, the change in volume can be calculated using the coefficient of linear expansion.

- **Buoyancy:** How objects float, based on Archimedes' principle. As the cube expands, its density relative to the mercury changes, affecting how much of it is submerged.

- **Density Changes:** How the density of the mercury might slightly change with temperature, also affecting buoyancy.

By understanding these concepts, one can solve for the additional sinking depth of the cube in the mercury.

Expert Solution

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Step 1: Determine relation between mercury density and sinking depth of cube.

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Step 2: Determine the change in depth.

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