An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be.
An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be.
- [JEE MAIN 2022]
- A
$\left[ ML ^{2} T ^{-2} \theta^{-1}\right]$
- B
$\left[ M ^{0} L ^{2} T ^{-2}\right]$
- C
$\left[ M ^{0} L ^{0} T ^{0}\right]$
- D
$\left[ M ^{0} L ^{2} T ^{0}\right]$
Similar Questions
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In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is
The density of a material in $CGS$ system of units is $4\, g\, cm^{-3}$ . In a system of units in which unit of length is $10\, cm$ and unit of mass is $100 \,g,$ the value of density of material will be
- [AIPMT 2011]
The dimension of stopping potential $\mathrm{V}_{0}$ in photoelectric effect in units of Planck's constant $h$, speed of light $c$, Gravitational constant $G$ and ampere $A$ is
- [JEE MAIN 2020]
A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?
$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$
$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$
$(C)$ $\frac{\text { Energy }}{\text { Volume }}$
$(D)$ $\frac{\text { Power }}{\text { Area }}$
A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?
$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$
$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$
$(C)$ $\frac{\text { Energy }}{\text { Volume }}$
$(D)$ $\frac{\text { Power }}{\text { Area }}$
- [IIT 2021]
Match List $I$ with List $II$
List $I$
List $II$
$A$ Spring constant
$I$ $(T ^{-1})$
$B$ Angular speed
$II$ $(MT ^{-2})$
$C$ Angular momentum
$III$ $(ML ^2)$
$D$ Moment of Inertia
$IV$ $(ML ^2 T ^{-1})$
Choose the correct answer from the options given below
Match List $I$ with List $II$
| List $I$ | List $II$ |
| $A$ Spring constant | $I$ $(T ^{-1})$ |
| $B$ Angular speed | $II$ $(MT ^{-2})$ |
| $C$ Angular momentum | $III$ $(ML ^2)$ |
| $D$ Moment of Inertia | $IV$ $(ML ^2 T ^{-1})$ |
Choose the correct answer from the options given below
- [JEE MAIN 2023]