Question 102: Properties of Matter

Question

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

Accepted Answer

$[v]=\left[\mathrm{T}^{-1}ight]$
$
\begin{aligned}
& {[r]=\mathrm{L} \quad[s]=\left[\frac{\mathrm{MLT}^{-2}}{\mathrm{~L}}ight]} \\
& {[ho]=\left[\frac{\mathrm{M}}{\mathrm{L}^{3}}ight]=\left[\mathrm{ML}^{-3}ight]} \\
& \Rightarrow v=r^{a} ho^{b} \mathrm{~s}^{c} \\
& \Rightarrow \mathrm{T}^{-1}=\mathrm{L}^{a} \mathrm{M}^{b} \mathrm{~L}^{-3 b} \mathrm{M}^{c} \mathrm{~T}^{-2 c} \\
& \Rightarrow \mathrm{T}^{-1}=\mathrm{M}^{(b+c)} \mathrm{L}^{(a-3 b)} \mathrm{T}^{-2 c} \\
& -2 c=-1 \Rightarrow c=\frac{1}{2} \\
& b+c=0 \\
& \Rightarrow b=-\frac{1}{2} \\
& a-3 b=0 \Rightarrow 3 b=a \Rightarrow a=-\frac{3}{2} \\
& (a, b, c)=\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}ight)
\end{aligned}
$

Answer

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

Answer

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

Answer

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

Answer

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

Properties of Matter

The frequency (\nu) 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 \nu=r^a\rho^b s^c. The values of a, b and c respectively are

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