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 $(a)$.

Standard 11

Physics

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An object falling through a fluid is observed to have acceleration given by $a = g -bv$ where $g =$ gravitational acceleration and $b$ is constant. After a long time of release, it is observed to fall with constant speed. The value of constant speed is

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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 $t$ ?

Solution

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