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. $v^{2}rg$

A force F is given by F = at + bt², where t is time. What are the dimensions of a and b:

1. $ML{T}^{-3}$ and $M{L}^2{T}^{-4}$

2. $ML{T}^{-3}$ and $ML{T}^{-4}$

3. $ML{T}^{-1}$ and $ML{T}^0$

4. $ML{T}^{-4}$ and $ML{T}^1$

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

If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is 

1. $c^2{g}^0{p}^{-2}$

2. $c^0{g}^2{p}^{-1}$

3. $c{g}^3{p}^{-2}$

4. $c^{-1}{g}^0{p}^{-1}$

If the time period (T) of vibration of a liquid drop depends on surface tension (S), radius (r) of the drop and density $\left(\rho \right)$ of the liquid, then the expression of T is 

1. $T=k\sqrt{\rho r^3/S}$

2. $T=k\sqrt{{\rho }^{1/2}{r}^3/S}$

3. $T=k\sqrt{\rho r^3/S^{1/2}}$

4. None of these

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

1. Surface tension

2. Solar constant

3. Density

4. Compressibility

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

The dimensions of the interatomic force constant are:

1. $M{T}^{-2}$

2. $ML{T}^{-1}$

3. $ML{T}^{-2}$

4. $M{L}^{-1}{T}^{-1}$