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Which of the following equations is dime...

Which of the following equations is dimensionally incorrect ?
Where t=time, h = height, s = surface tension, `theta` = angle, p= density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, T = torque, `epsilon`=permittivity, E = electric field, J = current density, L = length.

A

`W = Gamma theta`

B

`v=(pip alpha^4)/(8etaL)`

C

`h=(2scos theta)/(rhorg)`

D

`J=epsilon=(delE)/(delt)`

Text Solution

Verified by Experts

The correct Answer is:
B
In option (a) `W= tau theta`
In option (b) `(pi pa^4)/(8etaL) = (dV)/(dt) =` Volumetric flow rate (Poiseuille.s law)
In option (c) hpg = `(2s)/r = cos theta`
In option (d) RHS `implies epsilonxx(1)/(4piepsilon_0)(a)/r^2xx1/epsilon=q/txx1/r^2`
`= I/L^2 = IL^(-2)`
LHS `=T =I/A =IL^(-2)`
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