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Q.

The critical velocity v of a body depends on the coefficient of viscosity $η$ the density d and radius of the drop r. If K is a dimensionless constant then v is equal to

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a

$\frac{K η}{dr}$

b

$\frac{Kr}{ηr}$

c

$\frac{{Kηd}^{r}}{r}$

d

$\frac{Kd}{ηr}$

answer is C.

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Detailed Solution

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$\begin{array}{l} {Vαη}^{a} r^{b} d^{c} \Rightarrow {LT}^{- 1} α {({ML}^{- 1} T^{- 1})}^{a} L^{b} {({ML}^{- 3})}^{c} \\ a + c = 0 & - a + b - 3 c = 1 \\ & - a = - 1 \Rightarrow a = 1 \\ c = - 1 \Rightarrow b = 1 + a + 3 c \\ = 1 + 1 + 3 (- 1) = - 1 \\ {Vαη}^{1} r^{- 1} d^{- 1} \Rightarrow V = \frac{kη}{rd} \end{array}$

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The critical velocity v of a body depends on the coefficient of viscosity η the density d and radius of the drop r. If K is a dimensionless constant then v is equal to