An expression for a dimensionless quantity $P$ is given by $P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)$; where $\alpha$ and $\beta$ are constants, $x$ is distance ; $k$ is Boltzmann constant and $t$ is the temperature. Then the dimensions of $\alpha$ will be
- [JEE MAIN 2022]
- A$[ M ^{0} L ^{-1} T ^{0} ]$
- B$[ ML ^{0} T ^{-2}]$
- C$[ MLT ^{-2}]$
- D$[ ML ^{2} T ^{-2}]$
Similar Questions
The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are
The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are
- [JEE MAIN 2023]
In the relation $y = a\cos (\omega t - kx)$, the dimensional formula for $k$ is
In the relation $y = a\cos (\omega t - kx)$, the dimensional formula for $k$ is
The conversion of $1 \;MW$ power in a new system having basic unit of mass, length and time as $10 \;kg , 1 \;dm$ and $1 \;minute$ respectively is:
Match List $I$ with List $II$
List $I$
List $II$
$(A)$ Young's Modulus $(Y)$
$(I)$ $\left[ M L ^{-1} T ^{-1}\right]$
$(B)$ Co-efficient of Viscosity $(\eta)$
$(II)$ $\left[ M L ^2 T ^{-1}\right]$
$(C)$ Planck's Constant $(h)$
$(III)$ $\left[ M L ^{-1} T ^{-2}\right]$
$(D)$ Work Function $(\phi)$
$(IV)$ $\left[ M L ^2 T ^{-2}\right]$
Choose the correct answer from the options given below:
Match List $I$ with List $II$
| List $I$ | List $II$ |
| $(A)$ Young's Modulus $(Y)$ | $(I)$ $\left[ M L ^{-1} T ^{-1}\right]$ |
| $(B)$ Co-efficient of Viscosity $(\eta)$ | $(II)$ $\left[ M L ^2 T ^{-1}\right]$ |
| $(C)$ Planck's Constant $(h)$ | $(III)$ $\left[ M L ^{-1} T ^{-2}\right]$ |
| $(D)$ Work Function $(\phi)$ | $(IV)$ $\left[ M L ^2 T ^{-2}\right]$ |
Choose the correct answer from the options given below:
- [JEE MAIN 2023]
With the usual notations, the following equation ${S_t} = u + \frac{1}{2}a(2t - 1)$ is
With the usual notations, the following equation ${S_t} = u + \frac{1}{2}a(2t - 1)$ is