Dimensional analysis is used to check the validity of an equation relating the speed of sound (v) in a gas to its pressure (P) and density (). Which limitation prevents dimensional analysis from distinguishing between and ?
It cannot determine dimensionless constants.
It cannot handle fractional exponents.
It assumes a linear relationship between variables.
It fails when more than three variables are involved.
Related Questions
If the formula for the velocity of a wave is given by , where is tension and is mass per unit length. Using dimensional analysis, which aspect of this formula cannot be derived?
The dimensions of velocity
The dimensions of tension
The dimensions of mass per unit length
That the relationship is a square root
Dimensional analysis can help in deriving relationships between physical quantities. However, it cannot:
Check the homogeneity of physical equations
Convert units from one system to another
Deduce the dimensions of a physical quantity
Distinguish between two physical quantities having the same dimensions
A student uses dimensional analysis to analyze the time () it takes for a capacitor (C) to discharge through a resistor (R). They correctly identify that depends on R and C. However, they are unable to derive the precise relationship . What limitation of dimensional analysis explains this?
Dimensional analysis cannot reveal purely numerical relationships between variables.
The analysis requires knowledge of the initial charge on the capacitor, which is not provided.
Dimensional analysis cannot handle exponential decay processes.
The relationship between , R, and C is logarithmic, not a power law.
The time period of a simple pendulum is given by . Dimensional analysis can help deduce this relationship except for:
The dependence of on and
The constant
The square root relationship
The inverse relationship with
In a vernier callipers, divisions on the vernier scale coincide with divisions on the main scale. If each division on the main scale is mm, find the vernier constant (in cm).
The vernier scale of a vernier callipers has divisions that coincide with divisions on the main scale. If the main scale is marked in millimeters, what is the least count of the instrument (in cm)?
A vernier callipers has divisions on the vernier scale coinciding with divisions on the main scale. If each division on the main scale is mm, what is the vernier constant (in cm)?
Which of the following cannot be determined using dimensional analysis?
Numerical value of a constant
Units of a physical quantity
Conversion of units
Consistency of a physical equation
Which of the following quantities cannot be determined using dimensional analysis?
Numerical value of a constant
Unit of a physical quantity
Conversion factor between different units
Relationship between different physical quantities
The relative density of the material of a body is the ratio of its weight in air and the loss of its weight in water. By using a spring balance, the weight of the body in air in measured to be 5.00 0.05N. The weight of the body in water is measured to be 4.00 0.05N. Then the maximum possible percentage error in relative density is
11%
1%
9%
7%
