Question

The physical quantities not having same dimensions are:

• A. torque and work
• B. momentum and Plancks constant
• C. stress and Youngs modulus
• D. speed and $({\mu }_0{\epsilon }_0{)}^{-1/2}$

Answer 1

The correct option is B momentum and Plancks constant

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

The stress and the young's modulus have the same dimensions because the young's modulus is defined as the ratio of stress and strain and strain is a dimensionless quantity.

The speed of an electromagnetic wave is given by $\frac{1}{{\mu }_0{ϵ}_0}$. so, both have the same dimension.

Dimensions of momentum $=$ kg $m/\sec =\left[ML{T}^{-2}\right]$

Dimensions of PIanck's constant $=$ joule $\sec =\left[M{L}^2{T}^{-1}\right]$

$\therefore$Dimensions of momentum $\ne$ dimensions of PIanck's constant.