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) ML^–1T^–1

(2) MLT^–1

(3) M⁰LT^–1

(4) ML⁰T^–1

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

The dimensional formula for Boltzmann's constant is 

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

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

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

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

The dimensions of K in the equation $W=\frac{1}{2}K{x}^2$ is 

(1) $M^1{L}^0{T}^{-2}$

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

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

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

The physical quantities not having the same dimensions are: 

(1) Speed and ${\left({\mu }_0{\epsilon }_0\right)}^{-1/2}$

(2) Torque and work

(3) Momentum and Planck's constant

(4) Stress and Young's modules

The dimensional formula of relative density is: 

(1) ML^–3

(2) LT^–1

(3) MLT^–2

(4) Dimensionless