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)
Create a free account to view solution
View Solution FreeTopic: Basic Maths and Units and Dimensions·Practice all Basic Maths and Units and Dimensions questions
More Basic Maths and Units and Dimensions Questions
A half ring of radius R has a charge of λ per unit length. The potential at the centre of the half ring is :-...With what speed should a body be thrown upwards so that the distance traversed in 7th second and 8th second are equal :-...A ring of mass M and radius R is rotating with angular speed w about a fixed vertical axis passing through its centre O ...A body of mass m slides down an incline and reaches the bottom with a velocity V. If the same mass were in form of ring ...Liquid rises to a height of 2cm in a capillary tube. The angle of contact between the solid and the liquid is zero. The ...