If dimensions of critical velocity $v_c$ of a liquid flowing through a tube are expressed as$ [\eta ^x \rho ^yr^z]$ 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

  • [AIPMT 2015]
  • A

    $1,1,1$

  • B

    $1,-1,-1$

  • C

    $-1,-1,1$

  • D

    $-1,-1,-1$

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  • [JEE MAIN 2024]

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