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If the number of fundamental dimensions equals 'm', then the repeating variables shall be equal to:
- a)m and none of the repeating variables shall represent the dependentvariable.
- b)m + 1 and one of the repeating variables shall represent the dependentvariable
- c)m + 1 and none of the repeating variables shall represent the dependentvariable.
- d)m and one of the repeating variables shall represent the dependent variable
Correct answer is option 'C'. Can you explain this answer?
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If the number of fundamental dimensions equals 'm', then the r...
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If the number of fundamental dimensions equals 'm', then the r...
Explanation:
The question is asking about the relationship between the number of fundamental dimensions (m) and the repeating variables in a system.
Repeating Variables:
Repeating variables are the variables that have the same dimensions as the fundamental dimensions. They represent the physical quantities that are involved in the system.
Fundamental Dimensions:
Fundamental dimensions are the base dimensions that are used to express all other dimensions in a system. For example, in the International System of Units (SI), the fundamental dimensions are length (L), mass (M), and time (T).
Dependent Variable:
The dependent variable is the variable that is being measured or observed in an experiment or study. It depends on the independent variables and can be influenced by them.
Option C:
According to option C, if the number of fundamental dimensions is equal to m, then the repeating variables shall be equal to m and none of the repeating variables shall represent the dependent variable.
Explanation of Option C:
In a system with m fundamental dimensions, there will be m repeating variables. This is because each fundamental dimension requires a corresponding repeating variable to represent it.
None of the repeating variables can represent the dependent variable because the dependent variable is not determined by the fundamental dimensions alone. It can also depend on other factors or independent variables that are not related to the fundamental dimensions.
For example, in the study of fluid flow, the fundamental dimensions are length (L), mass (M), and time (T). The repeating variables in this system would be velocity (L/T), pressure (M/LT^2), and density (M/L^3). None of these repeating variables represent the dependent variable, such as the flow rate or the viscosity, as these variables depend on other factors like the geometry of the system or the properties of the fluid.
Therefore, option C is correct. The repeating variables shall be equal to m, and none of the repeating variables shall represent the dependent variable.
The question is asking about the relationship between the number of fundamental dimensions (m) and the repeating variables in a system.
Repeating Variables:
Repeating variables are the variables that have the same dimensions as the fundamental dimensions. They represent the physical quantities that are involved in the system.
Fundamental Dimensions:
Fundamental dimensions are the base dimensions that are used to express all other dimensions in a system. For example, in the International System of Units (SI), the fundamental dimensions are length (L), mass (M), and time (T).
Dependent Variable:
The dependent variable is the variable that is being measured or observed in an experiment or study. It depends on the independent variables and can be influenced by them.
Option C:
According to option C, if the number of fundamental dimensions is equal to m, then the repeating variables shall be equal to m and none of the repeating variables shall represent the dependent variable.
Explanation of Option C:
In a system with m fundamental dimensions, there will be m repeating variables. This is because each fundamental dimension requires a corresponding repeating variable to represent it.
None of the repeating variables can represent the dependent variable because the dependent variable is not determined by the fundamental dimensions alone. It can also depend on other factors or independent variables that are not related to the fundamental dimensions.
For example, in the study of fluid flow, the fundamental dimensions are length (L), mass (M), and time (T). The repeating variables in this system would be velocity (L/T), pressure (M/LT^2), and density (M/L^3). None of these repeating variables represent the dependent variable, such as the flow rate or the viscosity, as these variables depend on other factors like the geometry of the system or the properties of the fluid.
Therefore, option C is correct. The repeating variables shall be equal to m, and none of the repeating variables shall represent the dependent variable.
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If the number of fundamental dimensions equals 'm', then the repeating variables shall be equal to:a)m and none of the repeating variables shall represent the dependentvariable.b)m + 1 and one of the repeating variables shall represent the dependentvariablec)m + 1 and none of the repeating variables shall represent the dependentvariable.d)m and one of the repeating variables shall represent the dependent variableCorrect answer is option 'C'. Can you explain this answer?
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