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A particle released from rest is falling through a thick fluid

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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 $t$ ?

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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

15 mins ago

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Text solutionVerified

Let the effective

g = g^{'}

Now we know

m g^{'} - α v^{2} = m \frac{d v}{d t}

Initially velocity will rise and later

m g^{'} = α v^{2}

then velocity will become constant .

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Question Text	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 $t$ ?
Answer Type	Text solution:1
Upvotes	150

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?

Text solutionVerified

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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 $t$ ?