Question

Identify the pair of physical quantities that have same dimensions :

• A. velocity gradient and decay constant
• B. wien’s constant and Stefan constant
• C. angular frequency and angular momentum
• D. wave number and Avogadro number

Answer 1

Answer: (A)

velocity gradient and decay constant

Answer 2

Velocity gradient

= $\frac{dv}{dx}$

⇒ Dimensions are

$\frac{[LT-1]}{[L]}=[T-1]$

Decay constant $λ$ has dimensions of $[T^{–1}]$ because of the relation

$\frac{dN}{dt} = -λN$

⇒ Velocity gradient and decay constant have same dimensions.