First slide

Dimensions of physical quantities

Question

A stone is lying at rest in a river. The minimum mass of stone, $m = k ρ v^{x} g^{- 3}$ is needed to remain at rest. Here, k = constant having no unit, g = acceleration due to gravity, v = river flow velocity , $ρ$ = density of water. The value of x is_________________

Moderate

Solution

The unit of LHS is kg. The unit of RHS should be kg.
$\begin{array}{l} Here, k ρ v^{x} g^{- 3} = (\frac{k g}{m^{3}}) {(\frac{m}{s})}^{x} {(\frac{m}{s^{2}})}^{- 3} = (kg) (m)^{- 3 + x - 3} (s)^{+ 6 - x} \\ ∴ - 6 + x = 0 \\ \Rightarrow x = 6 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App