Which of the following relation cannot be deduced using dimensional analysis? [the symbols have their usual meanings]
Which of the following relation cannot be deduced using dimensional analysis? [the symbols have their usual meanings]
- A
All of these
- B
$v=u+ at$
- C
$k=\frac{1}{2} m v^2$
- D
$y=A \sin (\omega t+k x)$
Similar Questions
Choose the correct match
List I
List II
$(i)$ Curie
$(A)$ $ML{T^{ - 2}}$
$(ii)$ Light year
$(B)$ $M$
$(iii)$ Dielectric strength
$(C)$ Dimensionless
$(iv)$ Atomic weight
$(D)$ $T$
$(v)$ Decibel
$(E)$ $M{L^2}{T^{ - 2}}$
$(F)$ $M{T^{ - 3}}$
$(G)$ ${T^{ - 1}}$
$(H)$ $L$
$(I)$ $ML{T^{ - 3}}{I^{ - 1}}$
$(J)$ $L{T^{ - 1}}$
Choose the correct match
|
List I |
List II |
|---|---|
|
$(i)$ Curie |
$(A)$ $ML{T^{ - 2}}$ |
|
$(ii)$ Light year |
$(B)$ $M$ |
|
$(iii)$ Dielectric strength |
$(C)$ Dimensionless |
|
$(iv)$ Atomic weight |
$(D)$ $T$ |
|
$(v)$ Decibel |
$(E)$ $M{L^2}{T^{ - 2}}$ |
|
$(F)$ $M{T^{ - 3}}$ |
|
|
$(G)$ ${T^{ - 1}}$ |
|
|
$(H)$ $L$ |
|
|
$(I)$ $ML{T^{ - 3}}{I^{ - 1}}$ |
|
|
$(J)$ $L{T^{ - 1}}$ |
- [IIT 1992]
Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :
List $I$
List $II$
$P.$ Boltzmann constant
$1.$ $\left[ ML ^2 T ^{-1}\right]$
$Q.$ Coefficient of viscosity
$2.$ $\left[ ML ^{-1} T ^{-1}\right]$
$R.$ Planck constant
$3.$ $\left[ MLT ^{-3} K ^{-1}\right]$
$S.$ Thermal conductivity
$4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$
Codes: $ \quad \quad P \quad Q \quad R \quad S $
Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :
| List $I$ | List $II$ |
| $P.$ Boltzmann constant | $1.$ $\left[ ML ^2 T ^{-1}\right]$ |
| $Q.$ Coefficient of viscosity | $2.$ $\left[ ML ^{-1} T ^{-1}\right]$ |
| $R.$ Planck constant | $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$ |
| $S.$ Thermal conductivity | $4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$ |
Codes: $ \quad \quad P \quad Q \quad R \quad S $
- [IIT 2013]
What is the dimensional formula of $a b^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.
- [JEE MAIN 2024]
In Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to .................
In Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to .................
- [JEE MAIN 2022]
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]