check whether the following equation is dimensionally correct h=2sigma.cosce, where h is the height of the liquid, r is the radius of tube, d is the density of liquid and g is the acceleration due to gravity.
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11th
Physics
Units and Measurement
Dimensions and Dimensional Analysis
Test if the following equat...
PHYSICS
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Asked on May 01, 2020 by
Iksha Mathu
Test if the following equation is dimensionally correct.
h=
ρrg
2Scosθ
.
where h=height, S=surface tension, ρ= density, P= pressure, V=volume, η= coefficient of viscosity, v= frequency and I=moment of inertia.
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ANSWER
h=
ρrg
2Scosθ
LHS=[L]
Surface tension =S=F/I=
L
MLT
−2
=[MT
−2
]
Density =ρM/V=[ML
−3
T
0
]
Radius =r=[L],g=[LT
−2
]
RHS=
ρrg
2Scosθ
=
[ML
−3
T
0
][L][LT
−2
]
[MT
−2
]
=[M
0
L
1
T
0
]=[L]
LHS=RHS
So, the relation is correct.
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