Viscous Force on Falling Object – Rankers Physics
Topic: Solid and Fluids
Subtopic: Surface Tension and Viscosity

Viscous Force on Falling Object

An object of mass m and density \(\rho\) is falling in a viscous liquid of density \(\frac{\rho}{4}\). When it attains terminal velocity, then viscous force acting on it will be:
\(\frac{mg}{4}\)
\(\frac{3mg}{4}\)
\(\frac{mg}{3}\)
3mg

Solution:

At terminal velocity, the upward forces balance the downward force: \(F_v + F_b = mg\). Since buoyant force is \(F_b = V \rho_l g = \left(\frac{m}{\rho}\right)\left(\frac{\rho}{4}\right)g = \frac{mg}{4}\), we get \(F_v = mg - \frac{mg}{4} = \frac{3mg}{4}\).

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