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Consider the motion of a small spherical...

Consider the motion of a small spherical steel body of mass m, falling freely through a long column of a fluid that opposes its motion with a force proportional to its speed. Initially, the body moves down fast, but after some time attains a constant velocity known as terminal velocity. If weight mg, opposing force (F,) and buoyant force (Fb) act on the body, then the correct equation relating these forces, after the terminal velocity is reached, is :

A

`mg + F_v = F_b`

B

`mg + F_v - F_b`

C

`mg = F_v + F_b`

D

None

Text Solution

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The correct Answer is:
C
Consider the situation given in the question. If we draw the free body diagram as per the given situation we will get it as follows:

Form the diagram, it can be seen that buoyancy force is net upward force where, `F_v` = Opposing force
`F_b` = Buoyancy force
Weight of ball = mg
So, `mg = F_b + F_v`
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