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Units and Measurement question

2015 · Q150
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Units and Measurement question

2015 · Q150

NEETPhysicsUnits and MeasurementMCQ+4 / −1
If dimensions of critical velocity υ\upsilonυc of a liquid flowing through a tube are expressed as [ηxρyrz]\left[ {{\eta ^x}{\rho ^y}{r^z}} \right][ηxρyrz] where η,ρ\eta ,\rhoη,ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by
  1. A
    −-−1, −-−1, −-−1
  2. B
    1, 1, 1
  3. C
    1, −-−1, −-−1
  4. D
    −-−1, −-−1, 1
View written solutionFree

Correct answer: C

υ\upsilon υc = [ηxρyrz]\left[ {{\eta ^x}{\rho ^y}{r^z}} \right][ηxρyrz]

Put dimensions of various quantities,

[M0LT-1] = [ML-1T-1]x [ML-3T0]y [M0LT0]z
                = [Mx + y L- x - 3y + z T- x]

Equating power both sides, we get

x + y = 0;
- x - 3y + z = 1;
- x = - 1

On solving, we get

x = 1, y = -1, z = -1

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