$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ 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
Bulk modulus
Modulus of rigidity
Compressibility
Energy density
What is Dimensional Analysis ? State uses of Dimensional Analysis.
The equation of a wave is given by$Y = A\sin \omega \left( {\frac{x}{v} - k} \right)$where $\omega $ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is
The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be
If momentum $(P)$, area $(A)$ and time $(T)$ are taken to be fundamental quantities then energy has dimensional formula
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 $