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Question

Which of the following is dimensionally correct? (ρ=density,η=coefficient of viscosity,P=pressure,S=surface tension,r=radius,g=gravitational constant)

A
h=2Scosθρ×rg
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B
v=Pρ
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C
V=Pr4tη
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D
none of the above
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Solution

The correct option is A h=2Scosθρ×rg
Dimensional formula of the following are given as-
S=MT2, g=LT2, ρ=ML3, r=L, h=L, v=LT1, P=ML1T2, t=T, η=ML1T1
Equating LHS and RHS of the following options :
(A) : LHS = L
RHS =[MT2][ML3][L][LT2]=[L]
LHS = RHS

(B) : LHS = LT1
RHS =[ML1T2]ML3=[L2T2]
LHS RHS

(C) : LHS = LT1
RHS =[ML1T2][L4][T][ML1T1]=[L4]
LHS RHS
Thus option A is correct.

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