Question

An iron ball of radius 0.3cm falls through a column of oil of density \[0.94g/c{m^3}\]. It is found to attain a terminal velocity of \[0.5{\text{ }}cm/s\]. Determine the viscosity of the oil. Given that the density of iron is \[7.8g/c{m^3}\]

Answer 1

Hint: Density is a measure of mass per volume. The average density of an object equals to its total mass divided by total volume. An object made from a comparatively thick material (such as iron) will have less volume than an object of equal mass made from some less thick substance
Terminal velocity is defined as the maximum velocity attainable by an object as it falls in a fluid. It occurs when the sum of the drag forces and the buoyancy is equal to downward forces of the gravity acting on the object

Complete step by step solution:
Here in the question they have given the radius of the iron ball that is $r = 0.3cm$ and they have also given the terminal velocity that is $v = 0.5cm/s$ and the density of the iron ball is given by $\rho = 7.8g/c{m^3}$
The density of oil (medium) is given by $\sigma = 0.94g/c{m^3}$
Now the terminal velocity acquired by ball is given by
${v_t} = \dfrac{{2(\rho - \sigma ){r^2}g}}{{9\eta }}$
Now we want the value of $\eta $so take it outside
$\eta = \dfrac{{2(\rho - \sigma ){r^2}g}}{{9{v_t}}}$
Now we have to substitute all the values in the above equation
$\eta = \dfrac{{2 \times (7.8 - 0.94) \times {{(0.3)}^2} \times 980}}{{9 \times 0.5}}$
After further calculation we get
$\eta = \dfrac{{2 \times 6.86 \times {{(0.3)}^2} \times 980}}{{9 \times 0.5}}$

After calculating the above equation we get final answer that is $\eta = 268.9$ Poise.

Note:The viscosity of a fluid is defined as a measure of its resistance to deformation at the given rate. For liquids, it corresponds to the informal concept of "thickness": the best example is, the syrup has a higher viscosity than water.
There are two types of viscosity commonly reported, dynamic and kinematic. Dynamic viscosity is the relationship between shear stress and the shear rate in a fluid. Kinematic viscosity is defined as the relationship between viscous and inertial forces in a fluid.