Question

Test if the following equations are dimensionally correct:
(a) h= 2Scosθ / ρrg
(b) v= (√p/ρ)
Concept of Physics - 1 , HC VERMA , Chapter "Introduction to Physics".

Answer 1

Hello Dear.

For part (a)  , h= 2Scosθ / ρrg

Dimensional formula for L.H.S:-
h= [L]

Dimensional formula for R.H.S:-
=2Scosθ /ρrg
= [S][cosθ] / [ρ][r][g]
= [MT⁻²](1) / [ML⁻³] [L][LT⁻²]
= [MT⁻²] / [ML⁻¹T⁻²]
=[L]

Hence L.H.S= R.H.S =L . 
so part (a) is dimensionally correct .
________________

For part (b) ,  v=  (√P/ρ)

Dimensional formula for L.H.S:-
v= d/t = [LT⁻¹]

Dimensional formula for R.H.S:-
=(√P/ρ) 
Where P is the pressure and ρ is the density.
= ( [ML⁻¹T⁻²] / [ML⁻³] )¹/²
= ( [L²T⁻²] )¹/²
= [LT⁻¹]
Hence L.H.S = R.H.S = LT⁻¹
so part (b) is dimensionally correct.


Hope it Helps.

Answer 2

this this is the answer to the first part of the quest thank you