$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be
$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be
- [JEE MAIN 2023]
- A
Bulk modulus
- B
Modulus of rigidity
- C
Compressibility
- D
Energy density
Similar Questions
A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is
A system has basic dimensions as density $[D]$, velocity $[V]$ and area $[A]$. The dimensional representation of force in this system is
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]
A dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta $ flowing per second through a tube of radius $r$ and length $l$ and having a pressure difference $p$ across its end, is
A dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta $ flowing per second through a tube of radius $r$ and length $l$ and having a pressure difference $p$ across its end, is
The dimensions of pressure are
The dimensions of pressure are
- [AIPMT 1990]
The fundamental unit which has the same power in the dimension formula of surface tension and viscosity is
The fundamental unit which has the same power in the dimension formula of surface tension and viscosity is