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3) For a constant hydraulic stress on an object, the fractional change in the object's volume (∆V/V) and its bulk modulus (B) are related as a) ∆V/V directly proportional to B b) ∆V/V directly proportional to 1/B c) ∆V/V directly proportional to B² d) ∆V/V directly proportional to 1/B²?
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3) For a constant hydraulic stress on an object, the fractional change...
Relationship between Volume Change and Bulk Modulus:
The fractional change in an object's volume (∆V/V) under a constant hydraulic stress is directly proportional to its bulk modulus (B). This relationship is crucial in understanding how materials respond to external pressure.
Definition of Bulk Modulus:
Bulk modulus is a measure of a material's resistance to uniform compression. It quantifies the amount of pressure needed to cause a unit fractional decrease in volume. Mathematically, bulk modulus (B) is defined as the ratio of hydraulic stress to the resulting fractional volume change.
Mathematical Relationship:
When a material is subjected to a constant hydraulic stress, the fractional change in volume (∆V/V) is directly proportional to the bulk modulus (B). This relationship is expressed as:
∆V/V ∝ B
Therefore, as the bulk modulus of a material increases, the fractional change in volume also increases proportionally. This means that materials with higher bulk moduli exhibit lower volume changes under the same amount of pressure compared to materials with lower bulk moduli.
Significance:
Understanding the relationship between volume change and bulk modulus is essential in various engineering applications. It helps in selecting appropriate materials for specific purposes based on their ability to withstand or accommodate volume changes under pressure. Additionally, this relationship is utilized in designing structures and systems that require stability and durability under varying stress conditions.
The fractional change in an object's volume (∆V/V) under a constant hydraulic stress is directly proportional to its bulk modulus (B). This relationship is crucial in understanding how materials respond to external pressure.
Definition of Bulk Modulus:
Bulk modulus is a measure of a material's resistance to uniform compression. It quantifies the amount of pressure needed to cause a unit fractional decrease in volume. Mathematically, bulk modulus (B) is defined as the ratio of hydraulic stress to the resulting fractional volume change.
Mathematical Relationship:
When a material is subjected to a constant hydraulic stress, the fractional change in volume (∆V/V) is directly proportional to the bulk modulus (B). This relationship is expressed as:
∆V/V ∝ B
Therefore, as the bulk modulus of a material increases, the fractional change in volume also increases proportionally. This means that materials with higher bulk moduli exhibit lower volume changes under the same amount of pressure compared to materials with lower bulk moduli.
Significance:
Understanding the relationship between volume change and bulk modulus is essential in various engineering applications. It helps in selecting appropriate materials for specific purposes based on their ability to withstand or accommodate volume changes under pressure. Additionally, this relationship is utilized in designing structures and systems that require stability and durability under varying stress conditions.
Community Answer
3) For a constant hydraulic stress on an object, the fractional change...
B=∆p×v/∆v option b
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3) For a constant hydraulic stress on an object, the fractional change in the object's volume (∆V/V) and its bulk modulus (B) are related as a) ∆V/V directly proportional to B b) ∆V/V directly proportional to 1/B c) ∆V/V directly proportional to B² d) ∆V/V directly proportional to 1/B²?
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3) For a constant hydraulic stress on an object, the fractional change in the object's volume (∆V/V) and its bulk modulus (B) are related as a) ∆V/V directly proportional to B b) ∆V/V directly proportional to 1/B c) ∆V/V directly proportional to B² d) ∆V/V directly proportional to 1/B²? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 3) For a constant hydraulic stress on an object, the fractional change in the object's volume (∆V/V) and its bulk modulus (B) are related as a) ∆V/V directly proportional to B b) ∆V/V directly proportional to 1/B c) ∆V/V directly proportional to B² d) ∆V/V directly proportional to 1/B²? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3) For a constant hydraulic stress on an object, the fractional change in the object's volume (∆V/V) and its bulk modulus (B) are related as a) ∆V/V directly proportional to B b) ∆V/V directly proportional to 1/B c) ∆V/V directly proportional to B² d) ∆V/V directly proportional to 1/B²?.
3) For a constant hydraulic stress on an object, the fractional change in the object's volume (∆V/V) and its bulk modulus (B) are related as a) ∆V/V directly proportional to B b) ∆V/V directly proportional to 1/B c) ∆V/V directly proportional to B² d) ∆V/V directly proportional to 1/B²? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 3) For a constant hydraulic stress on an object, the fractional change in the object's volume (∆V/V) and its bulk modulus (B) are related as a) ∆V/V directly proportional to B b) ∆V/V directly proportional to 1/B c) ∆V/V directly proportional to B² d) ∆V/V directly proportional to 1/B²? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3) For a constant hydraulic stress on an object, the fractional change in the object's volume (∆V/V) and its bulk modulus (B) are related as a) ∆V/V directly proportional to B b) ∆V/V directly proportional to 1/B c) ∆V/V directly proportional to B² d) ∆V/V directly proportional to 1/B²?.
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