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JEE Main 202228 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
28 June
Shift
Morning Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2022 · 28 June · Morning Shift · Physics · Units and Dimensions

Assertion A: Product of Pressure (P) and time (t) has the same...

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}

Options

  1. ABoth A and R true, and R is correct explanation of A.
  2. BBoth A and R are true but R is NOT the correct explanation of A.
  3. CA is true but R is false.
  4. DA is false but R is true.

Correct answer

C. A is true but R is false.

Step-by-step solution

Viscous force is given by F=ηA(dvdt)F = ηA\left(\dfrac{d v}{d t}\right), here, AA is area and dvdt\dfrac{d v}{d t} is velocity gradient.

Thus, η=FA(dvdt)η = \dfrac{F}{A\left(\dfrac{d v}{d t}\right)}.

Now, Pt=FAt=η(dvdt)tPt = \dfrac{F}{A}t = η\left(\dfrac{d v}{d t}\right)t

Then, \left[Pt\right] = M{L}^{- 1}{T}^{- 1} = \left[η\right]

Thus, assertion is true but reason is false.

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