Question

Check correctness of following formula by method of dimensions. V= root p/d, where P=pressure/time , d= density of medium and V= velocity.

Answer 1

Explanation:

Given,

$v = \sqrt{{ \frac{p}{t} }\div { \frac{m}{vol.} } }$

=>

$v = \sqrt{{pt}^{ - 1} (m \times {vol}^{ - 1}) }$

Now, Dimension (LHS) = [ LT-¹ ]

For the equation to be dimensionally correct,

Dim [ LHS ] = Dim [ RHS ]

Dim [ RHS ] = √ (M L-¹T-² × T-¹ × M L-³)

= √ ( M² L-⁴ T-³ )

= ( M L-² T-³/² )

Dim [ RHS ] is not equal to Dim [ LHS ]

So the equation is wrong