The frequency $(v)$ of an oscillating liquid drop may depend upon radius $(r)$ of the drop, density $(\rho)$ of liquid and the surface tension $(s)$ of the liquid as : $v=r^{ a } \rho^{ b } s ^{ c }$. The values of $a , b$ and $c$ respectively are

  • [JEE MAIN 2023]
  • A

    $\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$

  • B

    $\left(\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$

  • C

    $\left(\frac{3}{2}, \frac{1}{2},-\frac{1}{2}\right)$

  • D

    $\left(-\frac{3}{2}, \frac{1}{2}, \frac{1}{2}\right)$

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  • [IIT 2001]

Which of the following is not a dimensionless quantity?

  • [JEE MAIN 2021]

Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :

List $I$ List $II$
$P.$ Boltzmann constant $1.$ $\left[ ML ^2 T ^{-1}\right]$
$Q.$ Coefficient of viscosity $2.$ $\left[ ML ^{-1} T ^{-1}\right]$
$R.$ Planck constant $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$
$S.$ Thermal conductivity $4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$

Codes: $ \quad \quad P \quad Q \quad R \quad S $ 

  • [IIT 2013]

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