AIPMT | 2015Basic Maths and Units and DimensionsHard
Question
If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be :
Options
A.[EV-1T-2]
B.[EV-2T-2]
C.[E-2V-1T-3]
D.[EV-2T-1]
Solution
Applying dimensional analysis
S ∝ EaVbTc
M1L0T-2 = k [M1L2T-2]a[L1T-1]b[T1]c
M1L0T-2 = k [MaL2aT-2a][LbT-bTc
Comparision
a = 1
c = − 2
So the dimensional formula for surface tension will be [E1V-2T-2]
Alternate solution :
Surface Tension =
[Surface tension] =
= [E V-2T-2]
Hence option (2)
S ∝ EaVbTc
M1L0T-2 = k [M1L2T-2]a[L1T-1]b[T1]c
M1L0T-2 = k [MaL2aT-2a][LbT-bTc
Comparision
a = 1
c = − 2
So the dimensional formula for surface tension will be [E1V-2T-2]
Alternate solution :
Surface Tension =
[Surface tension] =
= [E V-2T-2]Hence option (2)
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