Units & Dimensions

JEE Main level, single correct, medium

90 of 149

Question 90 of 149

Assertion A: Product of Pressure (P)\left(P\right) and time (t)\left(t\right) has the same dimension as that of coefficient of viscosity.
Reason: Coefficient of viscosity =ForceVelocitygradient=\dfrac{Force}{Velocitygradient}

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Answer: (C) A is true but R is false.

Viscous force is given by F=ηA(dvdt)F=\eta A\left(\dfrac{dv}{dt}\right), here, AA is area and dvdt\dfrac{dv}{dt} is velocity gradient.
Thus, η=FA(dvdt)\eta =\dfrac{F}{A\left(\dfrac{dv}{dt}\right)}.
Now, Pt=FAt=η(dvdt)tPt=\dfrac{F}{A}t=\eta \left(\dfrac{dv}{dt}\right)t
Then, [Pt]=ML−1T−1=[η]\left[Pt\right]=M{L}^{-1}{T}^{-1}=\left[\eta \right]
Thus, assertion is true but reason is false.

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