The force of interaction between two atoms is given by $F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is
The force of interaction between two atoms is given by $F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);$ where $x$ is the distance, $k$ is the Boltzmann constant and $T$ is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is
- [JEE MAIN 2019]
- A
$M^0L^2T^{-4}$
- B
$M^2LT^{-4}$
- C
$MLT^{-2}$
- D
$M^2L^2T^{-2}$
Similar Questions
Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$.If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and a pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as
$\frac{v}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$
where, $k$ is a dimensionless constant. Correct value of $a, b$ and $c$ are
Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$.If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and a pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as
$\frac{v}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$
where, $k$ is a dimensionless constant. Correct value of $a, b$ and $c$ are
- [KVPY 2015]
If momentum $(P),$ area $(A)$ and time $(T)$ are taken to be the fundamental quantities then the dimensional formula for energy is :
- [JEE MAIN 2020]
Match List$-I$ with List$-II.$
List$-I$
List$-II$
$(a)$ Torque
$(i)$ ${MLT}^{-1}$
$(b)$ Impulse
$(ii)$ ${MT}^{-2}$
$(c)$ Tension
$(iii)$ ${ML}^{2} {T}^{-2}$
$(d)$ Surface Tension
$(iv)$ ${ML} {T}^{-2}$
Choose the most appropriate answer from the option given below :
| List$-I$ | List$-II$ |
| $(a)$ Torque | $(i)$ ${MLT}^{-1}$ |
| $(b)$ Impulse | $(ii)$ ${MT}^{-2}$ |
| $(c)$ Tension | $(iii)$ ${ML}^{2} {T}^{-2}$ |
| $(d)$ Surface Tension | $(iv)$ ${ML} {T}^{-2}$ |
- [JEE MAIN 2021]
If force $(F),$ velocity $(V)$ and time $(T)$ are taken as fundamental units, then the dimensions of mass are
If force $(F),$ velocity $(V)$ and time $(T)$ are taken as fundamental units, then the dimensions of mass are
- [AIPMT 2014]
A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^7 c^5$ and $n$ is a non-zero integer, then $(\alpha, \beta, \gamma, \delta)$ is given by
A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^7 c^5$ and $n$ is a non-zero integer, then $(\alpha, \beta, \gamma, \delta)$ is given by
- [IIT 2024]