Out of the following which pair of quantities do not have the same dimensions?

(1) Planck's constant and angular momentum

(2) Work and energy

(3) Pressure and Young's modulus

(4) Torque & moment of inertia

Identify the pair which has different dimensions:

(1) Planck's constant and angular momentum

(2) Impulse and linear momentum

(3) Angular momentum and frequency

(4) Pressure and Young's modulus

The dimensional formula $M^0{L}^2{T}^{-2}$ stands for

(1) Torque

(2) Angular momentum

(3) Latent heat

(4) Coefficient of thermal conductivity

Which of the following represents the dimensions of Farad 

(1) $M^{-1}{L}^{-2}{T}^4{A}^2$

(2) $M{L}^2{T}^2{A}^{-2}$

(3) $M{L}^2{T}^2{A}^{-1}$

(4) $M{T}^{-2}{A}^{-1}$

If L, C and R denote the inductance, capacitance and resistance respectively, the dimensional formula for C²LR is 

(1) $\left[M{L}^{-2}{T}^{-1}{I}^0\right]$

(2) $\left[M^0{L}^0{T}^3{I}^0\right]$

(3) $\left[M^{-1}{L}^{-2}{T}^6{I}^2\right]$

(4) $\left[M^0{L}^0{T}^2{I}^0\right]$

If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system is 

(1) $c^{1/2}{G}^{1/2}{h}^{1/2}$

(2) $c^{1/2}{G}^{1/2}{h}^{-1/2}$

(3) $c^{1/2}{G}^{-1/2}{h}^{1/2}$

(4) $c^{-1/2}{G}^{1/2}{h}^{1/2}$

Dimensions of charge are:

(1) $M^0{L}^0{T}^{-1}{A}^{-1}$

(2) MLTA^–1

(3) T^–1A

(4) TA

According to Newton, the viscous force acting between liquid layers of area A and velocity gradient $\Delta v/\Delta z$ is given by $F=-\eta A\frac{\Delta v}{\Delta z}$ where $\eta$ is constant called coefficient of viscosity. The dimension of $\eta$ are 

(1) $\left[M{L}^2{T}^{-2}\right]$

(2) $\left[M{L}^{-1}{T}^{-1}\right]$

(3) $\left[M{L}^{-2}{T}^{-2}\right]$

(4) $\left[M^0{L}^0{T}^0\right]$

Identify the pair whose dimensions are equal  

(1) Torque and work

(2) Stress and energy

(3) Force and stress

(4) Force and work

The dimensions of pressure are equal to:

(1) Force per unit volume

(2) Energy per unit volume

(3) Force

(4) Energy