Let $\left[{\epsilon }_0\right]$ denotes the dimensional formula of the permittivity of the vacuum and $\left[{\mu }_0\right]$ that of the permeability of the vacuum. If M = mass, L = length, T = Time and I = electric current, then 

1. $\left[{\epsilon }_0\right]=M^{-1}{L}^{-3}{T}^{2}I$

2. $\left[{\epsilon }_0\right]=M^{-1}{L}^{-3}{T}^4{I}^2$

3. $\left[{\mu }_0\right]=ML{T}^{-2}{I}^{-3}$

4. $\left[{\mu }_0\right]=M{L}^2{T}^{-1}I$

Dimensions of CR are those of 

(1) Frequency

(2) Energy

(3) Time period

(4) Current

The physical quantity that has no dimensions 

(1) Angular Velocity

(2) Linear momentum

(3) Angular momentum

(4) Strain

$M{L}^{-1}{T}^{-2}$ represents 

(1) Stress

(2) Young's Modulus

(3) Pressure

(4) All the above three quantities

Dimensions of magnetic field intensity is 

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

(2) $\left[ML{T}^{-1}{A}^{-1}\right]$

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

(4) $\left[ML{T}^{-2}A\right]$

The force F on a sphere of radius ‘a’ moving in a medium with velocity ‘v’ is given by $F=6\pi \eta av$. The dimensions of $\eta$ are 

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

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

(3) $ML{T}^{-2}$

(4) $M{L}^{-3}$

Which physical quantities have the same dimensions?

(1) Couple of force and work

(2) Force and power

(3) Latent heat and specific heat

(4) Work and power

Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful?

(1) A/B

(2) A + B

(3) A – B

(4) None

Given that v is speed, r is the radius and g is the acceleration due to gravity. Which of the following is dimensionless?

(1) $v^2/rg$

(2) $v^{2}r/g$

(3) $v^{2}g/r$

(4) $v^{2}rg$

The physical quantity which has the dimensional formula $M^1{T}^{-3}$ is 

(1) Surface tension

(2) Solar constant

(3) Density

(4) Compressibility