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Dimensional analysis is useful in
Dimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.
- a)checking the correctness of a physical equation
- b)determining the number of variables involved in a particular phenomenon
- c)determining the dimensionless groups from the given variables
- d)the exact formulation of a physical phenomenon
Correct answer is option 'C'. Can you explain this answer?
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Dimensional analysis is useful inDimensional analysis deals with the p...
Dimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.
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Dimensional analysis is useful inDimensional analysis deals with the p...
Dimensional analysis is a powerful tool used in the field of physics and engineering to analyze and understand the relationships between different physical variables involved in a phenomenon. It involves systematically arranging the important factors into dimensional groups, which helps in simplifying and solving complex equations. Dimensional analysis is particularly useful in determining dimensionless groups from given variables. Let's explore why option 'C' is the correct answer.
1. Checking the correctness of a physical equation:
Dimensional analysis can be used to check the correctness of a physical equation by ensuring that the dimensions of the variables on both sides of the equation are consistent. Each physical quantity has a specific dimension (e.g., length, mass, time), and if the dimensions on both sides of the equation do not match, then it indicates an error or inconsistency in the equation.
2. Determining the number of variables involved in a particular phenomenon:
Dimensional analysis can also help in determining the number of variables involved in a particular phenomenon. By analyzing the dimensions of the physical quantities, we can identify the independent variables that affect the phenomenon. This understanding is crucial in simplifying the problem and focusing on the key variables that need to be considered.
3. Determining the dimensionless groups from the given variables:
One of the primary applications of dimensional analysis is to determine dimensionless groups from given variables. Dimensionless groups are ratios of physical quantities with the same dimensions, and they have special significance in many physical phenomena. These dimensionless groups often represent fundamental relationships and can provide insights into the behavior of the system under study. By identifying and analyzing these dimensionless groups, engineers and scientists can derive meaningful conclusions and make predictions about the phenomenon.
4. The exact formulation of a physical phenomenon:
While dimensional analysis helps in simplifying and understanding the relationships between variables, it does not provide the exact formulation of a physical phenomenon. The exact formulation typically involves mathematical modeling, experimentation, and theoretical analysis. However, dimensional analysis can serve as a valuable initial step in formulating the problem and identifying the key variables and their relationships.
In conclusion, dimensional analysis is a powerful tool that can be used in various ways, including checking the correctness of a physical equation, determining the number of variables involved, and most importantly, determining dimensionless groups from given variables. This analysis helps in simplifying complex equations, understanding the behavior of the system, and making predictions about the phenomenon under study.
1. Checking the correctness of a physical equation:
Dimensional analysis can be used to check the correctness of a physical equation by ensuring that the dimensions of the variables on both sides of the equation are consistent. Each physical quantity has a specific dimension (e.g., length, mass, time), and if the dimensions on both sides of the equation do not match, then it indicates an error or inconsistency in the equation.
2. Determining the number of variables involved in a particular phenomenon:
Dimensional analysis can also help in determining the number of variables involved in a particular phenomenon. By analyzing the dimensions of the physical quantities, we can identify the independent variables that affect the phenomenon. This understanding is crucial in simplifying the problem and focusing on the key variables that need to be considered.
3. Determining the dimensionless groups from the given variables:
One of the primary applications of dimensional analysis is to determine dimensionless groups from given variables. Dimensionless groups are ratios of physical quantities with the same dimensions, and they have special significance in many physical phenomena. These dimensionless groups often represent fundamental relationships and can provide insights into the behavior of the system under study. By identifying and analyzing these dimensionless groups, engineers and scientists can derive meaningful conclusions and make predictions about the phenomenon.
4. The exact formulation of a physical phenomenon:
While dimensional analysis helps in simplifying and understanding the relationships between variables, it does not provide the exact formulation of a physical phenomenon. The exact formulation typically involves mathematical modeling, experimentation, and theoretical analysis. However, dimensional analysis can serve as a valuable initial step in formulating the problem and identifying the key variables and their relationships.
In conclusion, dimensional analysis is a powerful tool that can be used in various ways, including checking the correctness of a physical equation, determining the number of variables involved, and most importantly, determining dimensionless groups from given variables. This analysis helps in simplifying complex equations, understanding the behavior of the system, and making predictions about the phenomenon under study.
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Dimensional analysis is useful inDimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.a)checking the correctness of a physical equationb)determining the number of variables involved in a particular phenomenonc)determining the dimensionless groups from the given variablesd)the exact formulation of a physical phenomenonCorrect answer is option 'C'. Can you explain this answer?
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Dimensional analysis is useful inDimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.a)checking the correctness of a physical equationb)determining the number of variables involved in a particular phenomenonc)determining the dimensionless groups from the given variablesd)the exact formulation of a physical phenomenonCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Dimensional analysis is useful inDimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.a)checking the correctness of a physical equationb)determining the number of variables involved in a particular phenomenonc)determining the dimensionless groups from the given variablesd)the exact formulation of a physical phenomenonCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Dimensional analysis is useful inDimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.a)checking the correctness of a physical equationb)determining the number of variables involved in a particular phenomenonc)determining the dimensionless groups from the given variablesd)the exact formulation of a physical phenomenonCorrect answer is option 'C'. Can you explain this answer?.
Dimensional analysis is useful inDimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.a)checking the correctness of a physical equationb)determining the number of variables involved in a particular phenomenonc)determining the dimensionless groups from the given variablesd)the exact formulation of a physical phenomenonCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Dimensional analysis is useful inDimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.a)checking the correctness of a physical equationb)determining the number of variables involved in a particular phenomenonc)determining the dimensionless groups from the given variablesd)the exact formulation of a physical phenomenonCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Dimensional analysis is useful inDimensional analysis deals with the process whereby all the important factors involved in a physical phenomenon are systematically arranged into dimensional group.a)checking the correctness of a physical equationb)determining the number of variables involved in a particular phenomenonc)determining the dimensionless groups from the given variablesd)the exact formulation of a physical phenomenonCorrect answer is option 'C'. Can you explain this answer?.
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