**Problem 2: Sphere Tension in Liquids**A sphere with a diameter of 35 cm and a density (\(\rho\)) of 450 kg/m\(^3\) is suspended by a cable. The sphere is submerged such that half of it is in a liquid with a density of 1200 kg/m\(^3\), while the other half is in a liquid with a density of 1500 kg/m\(^3\).**Objective**: Determine the tension in the cable.**Diagram Explanation**:The diagram presents the setup of the problem:- A solid sphere is suspended from a cable, partially submerged in two different liquids.- The sphere is divided into two parts: - The upper half is submerged in the liquid with a density of 1200 kg/m\(^3\). - The lower half is submerged in the liquid with a density of 1500 kg/m\(^3\).- Several force vectors are illustrated: - \(F_{B_{\rho=1200 \, \text{kg/m}^3}}\): Buoyant force exerted by the liquid with a density of 1200 kg/m\(^3\). - \(F_{B_{\rho=1500 \, \text{kg/m}^3}}\): Buoyant force exerted by the liquid with a density of 1500 kg/m\(^3\). - \(F_{g}\): Gravitational force on the sphere.- A vertical line with a length label of 120 cm indicates the distance from the top to the bottom of the submerged portion.**Key Concept**: To solve for the tension in the cable, apply the principles of buoyancy and equilibrium:1. Calculate the gravitational force.2. Determine the buoyant forces exerted by each liquid.3. Use the equilibrium condition to find the tension in the cable (sum of forces must be zero).

The free-body diagram is as follows-Where,T=tension in the cableW=weight of the spherebuoyancy…

2. A 35 cm diameter solid sphere (p=450 kg/m³) is Suspended by a cable as shown below. Half of the sphere is one fluid (p = 1200 kg/m³) and the other half is in another (p = 1500 kg/m³) What is the tension in the cable? FB. p=1200 kg/m³ FB₂ Bp=1500 kg/m³ Fgp=1200 kg/m³ p=1500 kg/m³ 120 cm

2. A 35 cm diameter solid sphere (p=450 kg/m³) is Suspended by a cable as shown below. Half of the sphere is one fluid (p = 1200 kg/m³) and the other half is in another (p = 1500 kg/m³) What is the tension in the cable? FB. p=1200 kg/m³ FB₂ Bp=1500 kg/m³ Fgp=1200 kg/m³ p=1500 kg/m³ 120 cm

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

Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.

Question

**Problem 2: Sphere Tension in Liquids**

A sphere with a diameter of 35 cm and a density (\(\rho\)) of 450 kg/m\(^3\) is suspended by a cable. The sphere is submerged such that half of it is in a liquid with a density of 1200 kg/m\(^3\), while the other half is in a liquid with a density of 1500 kg/m\(^3\).

**Objective**: Determine the tension in the cable.

**Diagram Explanation**:

The diagram presents the setup of the problem:

- A solid sphere is suspended from a cable, partially submerged in two different liquids.
- The sphere is divided into two parts:
- The upper half is submerged in the liquid with a density of 1200 kg/m\(^3\).
- The lower half is submerged in the liquid with a density of 1500 kg/m\(^3\).
- Several force vectors are illustrated:
- \(F_{B_{\rho=1200 \, \text{kg/m}^3}}\): Buoyant force exerted by the liquid with a density of 1200 kg/m\(^3\).
- \(F_{B_{\rho=1500 \, \text{kg/m}^3}}\): Buoyant force exerted by the liquid with a density of 1500 kg/m\(^3\).
- \(F_{g}\): Gravitational force on the sphere.
- A vertical line with a length label of 120 cm indicates the distance from the top to the bottom of the submerged portion.

**Key Concept**:

To solve for the tension in the cable, apply the principles of buoyancy and equilibrium:
1. Calculate the gravitational force.
2. Determine the buoyant forces exerted by each liquid.
3. Use the equilibrium condition to find the tension in the cable (sum of forces must be zero).

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