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# After terminal velocity is reached the acceleration of a body falling through a viscous fluid is:A) zero B) equal to gC) less than gD) greater than g

Last updated date: 19th Jun 2024
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Hint The terminal velocity of a body is reached when the viscous drag force faced by the body matches the force due to gravitational acceleration. At this point, there is no net force on the body and we can use Newton’s second law to determine the acceleration.

When an object is falling in a liquid, it experiences a viscous drag force due to the friction experienced by the object with the interaction with the liquid. The viscous force $F$ experienced by the particle of mass $m$ increases linearly with the velocity $v$ of the object $F = bv$ where $b$ is a constant.
When an object Is falling, it is accelerated due to gravity according to the relation $F = mg$ where $g$ is the gravitational acceleration on Earth. However, as its velocity rises, it will also experience more viscous force, and eventually, at one point the friction force and the buoyancy of the object will balance the force due to gravity and the object can be said to have reached the terminal velocity.
$F = ma$ where $a$ is the acceleration,
As the net force $F$ is zero, the net acceleration of the object is also zero which corresponds to option (A).