QJEEM21Phc33a: JEE Main 2021 Physics - Class 11 JEEM21Phc33a Solution: Which of the following equations is dimensionally incorrect?…

Question

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Which of the following equations is dimensionally incorrect?

Where t = time, h = height, s = surface tension,

θ

= angle,

ρ

= density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, T = torque,

\in

= permittivity, E = electric field, J = current density, L = length.

Accepted Answer

(a)

\frac{π p a^{4}}{8 η L} = \frac{d v}{d t}

= Volumetric flow rate (Poiseuille's law)

(b)

h ρ g = \frac{2 s}{r} \cos θ

(c)

ε \times \frac{1}{4 π ε_{0}} \frac{a}{r^{2}} \times \frac{1}{ε} = \frac{q}{t} \times \frac{1}{r^{2}}

= \frac{1}{L^{2}} = I L^{- 2}

LHS

T = \frac{I}{A} = I L^{- 2}

(d) W =

τ

θ

Option (a)

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