An object falling through a fluid is observed to have acceleratio… - Vidyadip

Question

An object falling through a fluid is observed to have acceleration given by a = g - bv where g = gravitational acceleration and b is constant. After a long time of release, it is observed to fall with constant speed. What must be the value of constant speed?

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Answer

Key concept: If a spherical body of radius r is dropped in a viscous fluid, it is first accelerated and then its acceleration becomes zero and it attains a constant velocity called terminal velocity.
According to the problem, acceleration of object is given by the relation
a = g - bv
When speed becomes constant acceleration $\text{a}=\frac{\text{dv}}{\text{dt}}=0$ (uniform motion).
where, g = gravitational acceleration
Clearly, from above equation as speed increases acceleration will decrease. At a certain speed say v₀, acceleration will be zero and speed will remain constant.
Hence, $\text{a}=\text{g}-\text{bv}_0=0$
$\Rightarrow\text{v}_0=\frac{\text{g}}{\text{b}}$

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