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  4. A spherical ball of iron of radius 2 mm is falling through a column of glycerine. If densities of glycerine and iron are respectively 1.3 × 103 kg / m 3 and 8 × 103 kg / m 3. η for glycerine =0.83 Nm -2 sec, then the terminal velocity is

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Q. A spherical ball of iron of radius $2 \,mm$ is falling through a column of glycerine. If densities of glycerine and iron are respectively $1.3 \times 10^3\, kg / m ^3$ and $8 \times 10^3 \,kg / m ^3$. $\eta$ for glycerine $=0.83\, Nm ^{-2} sec$, then the terminal velocity is

Mechanical Properties of Fluids

Solution:

Terminal velocity, $v _0=\frac{2 r ^2\left(\rho-\rho_0\right) g }{9 \eta}$
$=\frac{2 \times\left(2 \times 10^{-3}\right)^2 \times(8-1.3) \times 10^3 \times 9.8}{9 \times 0.83}=0.07 \,ms ^{-1}$