Question

The viscous force $F$ acting on a rain drop of radius '$a$' falling through air of coefficient of viscosity ${}^{\prime }{\eta }^{\prime }$ with terminal velocity $V$ is given by $F$ $\alpha$ $n^x{a}^y{V}^z$. The values of $x,y$ and $z$ are :

• A. -1, 2, 3
• B. -1, -1, -1
• C. 1, 2, 3
• D. 1, 1, 1

Answer 1

The correct option is D 1, 1, 1

$F\propto {\eta }^x{a}^y{v}^z$

$\eta$ $=\frac{F}{A\left(\frac{dv}{dx}\right)}=\frac{M^1{L}^1{T}^{-2}}{\left(L^2\right)\left(\frac{L{T}^{-1}}{L^1}\right)}=M^1{L}^{-1}{T}^{-1}$

$a=L^1$

$V=L{T}^{-1}$

$\Rightarrow F=\left(M^1{L}^{-1}{T}^{-1}{)}^x\right(L^1{)}^y(L{T}^{-1}{)}^z$

$M^1{L}^1{T}^{-2}=F=M^x{L}^{-x+y+z}{P}^{-x-g}$

$x=1$

$-x-z=-2\Rightarrow z=1$

$-x+y+z=1\Rightarrow y=1$

$\Rightarrow x=1=y=z$