Question

The physical quantities not having same dimensions are

• A. torque and work
• B. momentum and Planck’s constant
• C. Stress and Young’s modulus
• D. Speed and ${\left({\mu }_0{\epsilon }_0\right)}^{-\frac{1}{2}}$

Answer 1

The correct option is B

momentum and Planck’s constant

Explanation for the correct option:

In the case of option B,

1. The dimensional formula of momentum is = $\left[ML{T}^{-1}\right]$
2. The dimensional formula of Planck’s constant is = $\left[M{L}^2{T}^{-1}\right]$
3. Thus, momentum and Planck's constant have different dimensional formula.

Explanation for the incorrect options:

In the case of option A,

1. The dimensional formula of Torque $\left[M{L}^2{T}^{-2}\right]$.
2. The dimensional formula of work = $\left[M{L}^2{T}^{-2}\right]$.
3. Thus, torque and work have the same dimensions.

In the case of option C,

1. The dimensional formula of Stress and Young’s modulus = $\left[M{L}^{-1}{T}^{-2}\right]$.

In the case of option D,

1. The dimensional formula for Speed and ${\left({\mu }_0{\epsilon }_0\right)}^{-\frac{1}{2}}$ is $\left[M^0{L}^1{T}^{-1}\right]$.

Hence option B is the correct answer.