Question : Check the correctness of the relation h=2σcosθ/r2dg, where h is height, σ is surface Tension, θ is angle of contact, r is radius, d is density and g is acceleration due to gravity.
Doubt by Niyati
Solution :
We know,
Dimensions of
Height (h) = [L]
We know,
Dimensions of
Height (h) = [L]
Surface Tension (σ) = [ML0T-2]
Angle of Contact (θ) = [M0L0T0] = 1
Radius (r) = [L]
Angle of Contact (θ) = [M0L0T0] = 1
Radius (r) = [L]
Density [d] = [ML-3]
Acceleration due to gravity [g] = [LT-2]
h=2σcosθ/r2dg
LHS
Dimension of h
= [L]
= [M0L1T0]
LHS
Dimension of h
= [L]
= [M0L1T0]
RHS
Dimension of {2σcosθ/r2dg}
=[ML0T-2][M0L0T0]/[L]2[ML-3][LT-2]
=[MT-2]/[ML2-3+1T-2]
=[MT-2]/ML0T-2]
=[M1-1L0T-2+2]
= [M0L0T0]
Dimension of LHS ≠ Dimensions of RHS
=[MT-2]/[ML2-3+1T-2]
=[MT-2]/ML0T-2]
=[M1-1L0T-2+2]
= [M0L0T0]
Dimension of LHS ≠ Dimensions of RHS
Hence, the given equation is dimensionally not correct.