Fluid Mechanics

JEE Main level, numerical answer, medium

163 of 192

Question 163 of 192

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s20 \mathrm{~cm} / \mathrm{s}. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ____\_\_\_\_ cm/s\mathrm{cm} / \mathrm{s}.

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Answer: 5

For a sphere in a viscous fluid, terminal velocity is proportional to r2r^2: vt∝r2v_t \propto r^2.
For two balls of the same material in the same fluid: vt1vt2=r12r22\frac{v_{t1}}{v_{t2}} = \frac{r_1^2}{r_2^2}.
Given r1=6r_1 = 6 mm, vt1=20v_{t1} = 20 cm/s, and r2=3r_2 = 3 mm: 20vt2=369=4\frac{20}{v_{t2}} = \frac{36}{9} = 4.
Therefore, vt2=5v_{t2} = 5 cm/s.

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