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Question: Answered & Verified by Expert
A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in figure, indicate the one that represents the velocity $(v)$ of the pebble as a function of time $(t)$.
PhysicsMechanical Properties of Fluids
Options:
  • A

  • B

  • C

  • D

Solution:
2045 Upvotes Verified Answer
The correct answer is:

When the pebble is dropped from the top of cylinder filled with viscous oil and pebble falls under gravity with constant acceleration, but as it is dropped it enter in oil. So dragging or viscous force is
$$
F=6 \pi \eta r v
$$
where $r$ is radius of the pebble, $v$ is instantaneous speed, $\eta$ is coefficient of viscosity.
As the force is variable, hence acceleration is also variable so $v-t$ graph will not be straight line due to viscosity of oil. First velocity increases and then becomes constant known as terminal velocity.

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