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  4. Calculate the viscosity of glycerine if a ball of 2mm radius whose density is 8g/cm3 acquires a terminal velocity of 4cm/s while falling in the tank full of glycerine. (Density of glycerine is 1.3g/cm3 )

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Q. Calculate the viscosity of glycerine if a ball of $2mm$ radius whose density is $8g/cm^{3}$ acquires a terminal velocity of $4cm/s$ while falling in the tank full of glycerine. (Density of glycerine is $1.3g/cm^{3}$ )

NTA AbhyasNTA Abhyas 2020

Solution:

$v_{r}=\frac{2}{9}\frac{g \left(\right. \rho - \sigma \left.\right) r^{2}}{\eta}$ i.e., $\eta=\frac{2}{9}\frac{g \left(\right. \rho - \sigma \left.\right) r^{2}}{v_{T}}$
So, $\eta=\frac{2}{9}\times \frac{980 \times \left(\right. 8 - 1 . 3 \left.\right) \times \left(\right. 0 . 2 \left(\left.\right)^{2}}{4}=14.6Poise$ .