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. \(\left[c^{1/2}G^{1/2}h^{1/2}\right]\)
2. \(\left[c^{1/2}G^{1/2}h^{-1/2}\right]\)
3. \(\left[c^{1/2}G^{-1/2}h^{1/2}\right]\)
4. \(\left[c^{-1/2}G^{1/2}h^{1/2}\right]\)

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

Which of the two have the same dimensions?

1. Force and strain

2. Force and stress

3. Angular velocity and frequency

4. Energy and strain

An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then the dimension of the constant of proportionality is:
1. \(\left[ML^{-1}T^{-1}\right]\)

2. \(\left[MLT^{-1}\right]\)

3. \(\left[M^0LT^{-1}\right]\)

4. \(\left[ML^0T^{-1}\right]\)

The dimensions of emf in MKS are-

1. $\left[M^0{L}^2{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$

2. $\left[{\mathrm{ML}}^1{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$

3. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{A}}^{-1}\right]$

4. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$

Which of the following quantities is dimensionless

1. Gravitational constant

2. Planck's constant

3. Power of a convex lens

4. None