Surface Tension and Viscosity: Practice Problem & Solution
The velocity of a small ball of mass $M$ and density $d$, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $\frac{d}{2}$, then the viscous force acting on the ball will be: (2021)
Solution Explained:
To solve this problem, we apply the core principles of Surface Tension and Viscosity. Understanding the underlying formula is key to arriving at the correct answer below:
At constant terminal velocity, net force is zero. Viscous force $F_v = \text{Weight} - \text{Buoyant force}$. $$F_v = Vdg - V\left(\frac{d}{2}\right)g = \frac{Vdg}{2} = \frac{Mg}{2}$$.
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