Dimensional Analysis

Which of the following pairs does not have similar dimensions?

Which of the following units denotes the dimensions $\frac{M{L}^2}{Q^2}$, where $Q$ denotes the electric charge?

A sheet of area $40{ \mathrm{m}}^2$ is used to make an open tank with a square base, then find the dimensions of the base such that volume of this tank is maximum.

A quantity $X$ is given by ${\epsilon }_{0}L\frac{\Delta V}{\Delta t}$ where, ${\epsilon }_0$ is the permittivity of free space, $L$ is length, $\Delta V$ is potential difference and $\mathrm{\Delta }t$ is time interval. The dimensional formula for $X$ is the same as that of,

A neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by ${\mu }_0^x{m}^y{\omega }^2{c}^u,$ where ${\mu }_n$ and $c$ are the permeability and speed of light in free space, respectively. Then

A new temperature scale uses $X$ as a unit of temperature, where the numerical value of the temperature $t_{\mathrm{x}}$ in this scale is related to the absolute temperature $T$ by $t_{\mathrm{x}}=3T+300$. If the specific heat of material using this unit is $1400 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{X}}^{-1}$ its specific heat in the S.I. system of units is :

In $\mathrm{C}.\mathrm{G}.\mathrm{S}.$ system, the magnitude of the force is $100 \mathrm{dyne}.$ In another system where the fundamental physical quantities are kilogram, metre and minute, the magnitude of the force is

If $E=$ energy, $G=$ gravitational constant, $I=$ impulse and $M=$ mass, the dimension $\frac{G{I}^{2}M}{E^2}$ is same as that of,

If $A=B+\frac{C}{D+E},$ the dimensions of $B$ and $C$ are $\left[{\mathrm{M}}^0{\mathrm{LT}}^{-1}\right]$ and $\left[{\mathrm{M}}^0{\mathrm{LT}}^0\right],$ respectively. Find the dimensions of $A\mathit{,}\mathit{ }D$ and $\mathrm{E}$.

A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation $\left(T\right)$ of the liquid drop depends on radius $\left(r\right)$ of the drop, density $\left(\rho \right)$ and surface tension $\left(S\right)$ of the liquid. Which among the following will be a possible expression for $T$ (where, $k$is a dimensionless constant)?

If $R$ and $L$ denote resistance and inductance respectively which of the following has dimension of time?

A force $F$ is given by, $F=at+b{t}^2$, where $t$ is time. What are the dimensions of $a$ and $b$?

The dimensional equation for the electrical resistance of a conductor is

Among the following options, pick the one which has neither units nor dimensions.

If $Pressure = M^a{L}^b{T}^c$ , then value of  $a,b$and $c$ will be satisfied 

If $10 \mathrm{cm}$, $10 \mathrm{g}$ and  $0.1 \mathrm{s}$ are taken as the unit of length, mass and time respectively in particular system. Find the unit of force in this system as expressed in SI unit will be equivalent to

The dimensional formula $\sigma b^{\mathit{4}}$ (Here $\sigma \mathit{=}$ Stefan's constant and $b=$ Wein's constant) is

If the speed $v$ of a particle, of mass $m$, as a function of time $t$, is given by $v=\omega A\sin \left[\left(\sqrt{\frac{k}{m}}\right)t\right]$, where $A$ has dimension of length. Choose the correct option.

Which one of the following does not have the same dimensions?

Two quantities, $A$ and $B$ have different dimensions. Which mathematical operation, given below, is physically meaningful?