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

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 $ML{T}^1$

The dimensions of the interatomic force constant are:

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

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

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

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

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