Question

The physical quantities not having same dimensions are:

• A. Momentum and Planck's constant
• B. Stress and Young's modulus
• C. Speed and $({\mu }_0{ϵ}_0{)}^{-1/2}$
• D. Torque and work

Answer 1

Answer: (A)

The correct option is B Momentum and Planck's constant

The torque and the work both have the same dimensions because they are given as the product of force and the distance.

$\left[Momentum\right]=\left[ML{T}^{-1}\right]$

$\left[h\right]=\frac{E}{v}=M{L}^2{T}^{-2}T=\left[M{L}^2{T}^{-1}\right]$.

On the other hand, the young's modulus is the ratio of stress and strain. The strain is a dimensionless quantity. Therefore, the unit of stress and young's modulus will be the same.

The unit of speed is $m/s$ and it has the dimension of $\left[L{T}^{-1}\right]$.

The speed of light is given by:

$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$

Therefore, both will have the same dimensions.

So, option $\left(B\right)$ is correct.