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If dimensions of critical velocity \upsilon _\text{c} of a liquid flowing through a tube are expressed as \left[ {\eta ^x \rho ^y r^z } \right], where \eta, \rho 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 :

  • Option 1)

    -1, -1, 1

  • Option 2)

    -1, -1, -1

  • Option 3)

    1, 1, 1

  • Option 4)

    1, -1, -1

 

Answers (1)

best_answer

As we learned in concept

Percentage error in the value of x -

dpi{100} x= frac{left ( Delta a+Delta b ight )}{a-b} imes 100%

- wherein

Delta a= absolute error in measurement of a

Delta b= absolute error in measurement of b

Delta x= absolute error in measurement of x

 

Let [Vc] \propto [\eta]x [\delta]y[r]z 

Vc = critical velocity

[Vc] = [L1T-1]

[\eta] = [M1L-1T-1]

[\delta] =  [M1L-3]

[r] = [L]

equating dimensions of both sides.

1,-1, -1


Option 1)

-1, -1, 1

this is incorrect option

 

Option 2)

-1, -1, -1

this is incorrect option

Option 3)

1, 1, 1

this is incorrect option

Option 4)

1, -1, -1

this is correct option

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Plabita

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