A particle released from rest is falling through a thick fluid under gravity. fluid exerts a resisti

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9-1.Fluid Mechanics

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A particle released from rest is falling through a thick fluid under gravity. The fluid exerts a resistive force on the particle proportional to the square of its speed. Which one of the following graphs best depicts the variation of its speed $v$ with time $t$ ?

(KVPY-2012)

Solution

(a)

Velocity initially increases and this results in increase in resistive stokes force $(=6 \pi \eta r v)$.

After some time, resistive stokes force and force of buoyancy are equal to gravitational pull on the particle. After this instant velocity of particle becomes constant.

Hence, correct graph is $(a)$.

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