A student attempts to derive the formula for the period of a simple pendulum using dimensional analysis. They correctly identify the relevant variables as length (L), mass (m), and gravitational acceleration (g). Which of the following represents a fundamental limitation they will encounter?
Inability to determine the numerical constant in the formula.
Dimensional analysis cannot handle the trigonometric functions involved in the derivation.
Mass (m) is not a relevant variable for the period of a simple pendulum, making the analysis invalid.
Dimensional analysis can only be used for linear relationships between variables.
Related Questions
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
Which limitation of dimensional analysis prevents it from deriving the complete formula for the viscous force on a sphere moving through a fluid, given that the force (F) depends on the radius (r) of the sphere, its velocity (v), and the fluid's viscosity ()?
It cannot determine the numerical constant in Stokes' Law.
It fails to account for the turbulent flow regime.
It cannot handle the non-linear dependence on velocity at high Reynolds numbers.
It requires the density of the fluid, which is not provided.
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
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)?
Which of these equations, though dimensionally correct, might be physically incorrect due to limitations of dimensional analysis?
x = vt
v = at
x = vt + at
x = (1/2)at^2
A physicist uses dimensional analysis to derive an expression for the energy (E) of a particle based on its mass (m), velocity (v), and Planck's constant (h). They arrive at . Why is this result incomplete?
Dimensional analysis cannot account for dimensionless quantities like the fine-structure constant, which might be involved in a more complex relationship.
Planck's constant is not relevant for the energy of a classical particle, invalidating the analysis.
Dimensional analysis cannot handle situations involving both mass and velocity.
The correct expression involves a logarithmic relationship, which dimensional analysis cannot capture.
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)?
Dimensional analysis cannot be used to derive relationships containing:
Powers of quantities
Products of quantities
Ratios of quantities
Exponential functions
