A very small ball of radius r and mass m is released in a large tank having a liquid of density ρ and moving with an acceleration a as shown in figure. If coefficient of viscosity the liquid is η , th

Question

A very small ball of radius r and mass m is released in a large tank having a liquid of density ρ and moving with an acceleration a as shown in figure. If coefficient of viscosity the liquid is η , then terminal speed of the ball will be (neglect buoyant force) :

TestHub · Accepted Answer

In the accelerating tank's frame, effective gravity is $g^{2} + a^{2}$ .

At terminal speed, viscous drag balances the effective weight (buoyancy neglected):

$6 π ηr v = m g^{2} + a^{2}$

$v = \frac{m g ^{2} + a ^{2}}{6 π ηr}$ - (C)

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