Why concept of dimension has basic importance ?
Why concept of dimension has basic importance ?
Similar Questions
If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:
If $R , X _{ L }$. and $X _{ C }$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless:
- [JEE MAIN 2023]
From the equation $\tan \theta = \frac{{rg}}{{{v^2}}}$, one can obtain the angle of banking $\theta $ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is
From the equation $\tan \theta = \frac{{rg}}{{{v^2}}}$, one can obtain the angle of banking $\theta $ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is
Turpentine oil is flowing through a tube of length $l$ and radius $r$. The pressure difference between the two ends of the tube is $P .$ The viscosity of oil is given by $\eta=\frac{P\left(r^{2}-x^{2}\right)}{4 v l}$ where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are
Turpentine oil is flowing through a tube of length $l$ and radius $r$. The pressure difference between the two ends of the tube is $P .$ The viscosity of oil is given by $\eta=\frac{P\left(r^{2}-x^{2}\right)}{4 v l}$ where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are
- [AIPMT 1993]
The velocity of water waves $v$ may depend upon their wavelength $\lambda $, the density of water $\rho $ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as
The velocity of water waves $v$ may depend upon their wavelength $\lambda $, the density of water $\rho $ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as
Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$ : Time period of oscillation of a liquid drop depends on surface tension $(S)$, if density of the liquid is $p$ and radius of the drop is $r$, then $T = k \sqrt{ pr ^{3} / s ^{3 / 2}}$ is dimensionally correct, where $K$ is dimensionless.
Reason $(R)$: Using dimensional analysis we get $R.H.S.$ having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.
Assertion $(A)$ : Time period of oscillation of a liquid drop depends on surface tension $(S)$, if density of the liquid is $p$ and radius of the drop is $r$, then $T = k \sqrt{ pr ^{3} / s ^{3 / 2}}$ is dimensionally correct, where $K$ is dimensionless.
Reason $(R)$: Using dimensional analysis we get $R.H.S.$ having different dimension than that of time period.
In the light of above statements, choose the correct answer from the options given below.
- [JEE MAIN 2022]