WBJEE · Physics · Mechanical Properties of Fluids
Two spheres of the same material, but of radii \(R\) and \(3 R\) are allowed to fall vertically downwards through a liquid of density \(\rho\). The ratio of their terminal velocities is
- A \(1: 3\)
- B \(1: 6\)
- C \(1: 9\)
- D \(1: 1\)
Answer & Solution
Correct Answer
(C) \(1: 9\)
Step-by-step Solution
Detailed explanation
The terminal velocity, \(v=\frac{2 r^{2}(p-\sigma) g}{9 \eta}\) As, all other parameters are constant, therefore \(v\propto r^{2}\) \(\Rightarrow \quad \frac{v_{R}}{v_{3 R}}=\frac{(R)^{2}}{(3 R)^{2}}=\frac{1}{9}\)
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