What is dimensional analysis ? Write limitation of dimensional analysis.
What is dimensional analysis ? Write limitation of dimensional analysis.
$(1)$ In the dimensional equations containing $\mathrm{M}, \mathrm{L}$ and $\mathrm{T}$, we get at the best only three equations by equating the indices of $\mathrm{M}, \mathrm{L}$ and $\mathrm{T}$. Hence this method is of no avil in deducting the exact form of a physical relation which happens to depend upon more than three quantities.
$(2)$ The information about dimensionless constant cannot be obtained.
$(3)$ The equations containing exponential trigonometric functions lie quite outside the preview of this method.
$(4)$ This method is of no use if a constant of proportionally is not dimensionless.
Similar Questions
If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then
If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then
The dimension of stopping potential $\mathrm{V}_{0}$ in photoelectric effect in units of Planck's constant $h$, speed of light $c$, Gravitational constant $G$ and ampere $A$ is
- [JEE MAIN 2020]
If the capacitance of a nanocapacitor is measured in terms of a unit $u$ made by combining the electric charge $e,$ Bohr radius $a_0,$ Planck's constant $h$ and speed of light $c$ then
If the capacitance of a nanocapacitor is measured in terms of a unit $u$ made by combining the electric charge $e,$ Bohr radius $a_0,$ Planck's constant $h$ and speed of light $c$ then
- [JEE MAIN 2015]
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express mass, length and time in terms of dimensions of these quantities.
If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express mass, length and time in terms of dimensions of these quantities.
If force $(F),$ velocity $(V)$ and time $(T)$ are taken as fundamental units, then the dimensions of mass are
If force $(F),$ velocity $(V)$ and time $(T)$ are taken as fundamental units, then the dimensions of mass are
- [AIPMT 2014]