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9-1.Fluid Mechanics
hard
Which of the following is the incorrect graph for a sphere falling in a viscous liquid? (Given at $t = 0$, velocity $v = 0$ and displacement $x = 0$.)
A
B
C
D
Solution
A sphere falling in a viscous liquid increases its speed with time and finally achieves a terminal velocity at infinite time.
velocity varies with time as shown.
Net acceleration of the sphere is ($m g-$ Buoyant force$-$Viscous Force) downwards
$a=d \frac{4}{3} \pi R^{3} g-\rho \frac{4}{3} \pi R^{3} g-6 \pi \eta R v$
Hence a varies linearly with velocity. Hence option $\mathrm{C}$ is the correct answer.
Standard 11
Physics
