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Question
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).
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Solution
Explanation:
In fluids, when the pebble is dropped from the top of a tall cylinder filled with viscous oil, a variable force called viscous force will act which increases with an increase in speed. And at equilibrium this velocity becomes constant, that constant velocity is called terminal velocity.
When the pebble is falling through the viscous oil, the viscous force is F = 6πηrv
Where r is the radius of the pebble, v is instantaneous speed, η is the coefficient of viscosity. As the force is variable, hence acceleration is also variable so the v-t graph will not be a straight line. First velocity increases and then becomes constant known as terminal velocity.
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