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.
A highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly onto another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta $ such that the lower face of $A$ completely covers the upper face of $B$. The lower face of $B$is rigidly held on a horizontal surface. A small force $F$ is applied perpendicular to one of the side faces of $A$. After the force is withdrawn block $A$ executes small oscillations. The time period of which is given by
Which of the following quantities has a unit but dimensionless?
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 the time period $(T)$ of vibration of a liquid drop depends on surface tension $(S)$, radius $(r)$ of the drop and density $(\rho )$ of the liquid, then the expression of $T$ is