Question 86: 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

Choose the correct answer: