First slide

Viscosity

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).

Moderate

A
B
C
D

Solution

When the pebble is falling through the viscous oil the viscous force is $F = 6 πηrv$ where r is radius of the pebble, v is instantaneous speed, $η$ is coefficient of viscosity. As the force is variable, hence acceleration is also variable so v-t graph will not be straight line. First velocity increases and then becomes constant known as terminal velocity.

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