The frequency $\mathrm{n}$ of a tuning fork depends upon the length $l$ of the prong, the density $\mathrm{\rho }$ and the young's modulus $\mathrm{Y}$ of its material. From dimensional considerations, find a possible formula for the frequency of tuning fork.

 

The frequency $\mathrm{n}$ of an oscillating liquid drop may depend upon the radius $\mathrm{r}$ of the drop, density $\mathrm{\rho }$ and surface tension $S$ of the liquid. Obtain a formula for the frequency by the method of dimensions.

A liquid of density $\mathrm{\rho }$ is filled in a U-tube of uniform cross-section up to a height $\mathrm{h}$. If the liquid in one limb of the tube is pressed slightly downward and then left, the liquid column executes vertical oscillations. Assuming that the period $\mathrm{T}$ of oscillations may depend on $\mathrm{h}, \mathrm{\rho } \mathrm{and} \mathrm{g},$ find a possible formula for $\mathrm{T}$ by the method of dimensions.

In the following table there are two lists $\mathrm{A} \mathrm{and} \mathrm{B},$ but the list $\mathrm{B}$ is not in order of list $\mathrm{A}.$ Write down the list $\mathrm{B}$ in order of list $\mathrm{A}$ in each table : 

Match list $1$ with list $2$ and select the correct answer using the codes given below the lists :

:

Choose the 'dimensional' constant among the followings :

Dimension of $\frac{1}{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0},$ where symbol have their usual meanings, are :

In which of the following sets, the mentioned physical quantities have different dimensions?

A particles with initial velocity $\mathrm{u}$ is moving with uniform acceleration $\mathrm{a}.$ The distance moved by the particle in the ${\mathrm{t}}^{\mathrm{th}}$ second is given by $\mathrm{s}=\mathrm{u}+\frac{1}{2} \mathrm{a}\left(2\mathrm{t}-1\right).$ The dimension of $\mathrm{s}$ must be :