Units & Dimensions

JEE Main level, single correct, medium

99 of 149

Question 99 of 149

Which of the following equations is dimensionally incorrect?
Where
t=t=time, h=h=height, s=s=surface tension, θ=\theta =angle, ρ=\rho =density ,a,r=,a,r=radius, g=g= the acceleration due to gravity, V=V=volume, p=p=pressure, W=W=work done, τ=\tau =torque, ϵ=ϵ=permittivity, E=E=electric field, J=J=current density, L=L=length.

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Answer: (B) V=πpa48ηLV=\dfrac{\pi p{a}^{4}}{8\eta L}

Dimensions of πpa48ηL\dfrac{\pi p{a}^{4}}{8\eta L}(volume flow rate) is L3T–1{L}^{3}{T}^{–1}.

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