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 ${\left({\mu }_0{ϵ}_0\right)}^{-1/2}$

Answer 1

The correct option is B momentum and Plancks constant

$\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}=\sqrt{L^2{T}^{-2}}=L{T}^{-1}$
Speed $=L{T}^{-1}$
Stress, Young's modulus $=\frac{ML{T}^{-2}}{L^2}=M{L}^{-1}{T}^{-2}$
Momentum $=ML{T}^{-1}$
Torque, Work $=M{L}^2{T}^{-2}$
Planck's constant $=\frac{M{L}^2{T}^{-2}}{\left(L{T}^{-1}\right)}\times L=M{L}^2{T}^{-1}$
Hence, option B is correct.