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When small spherical bodies move through a viscous medium, the bodies drag the layers of the medium that are in contact with them. This dragging results in relative motion between different layers, which are away from the body. Therefore, a viscous drag comes into play, opposing the motion of the body. It is found that this backward force or viscous drag, increases with increase in velocity of the body.

According to Stoke, the viscous drag 'f'', depends on the coefficient of viscosity ' h ' of the medium, the velocity (v) of the body and radius (r) of the spherical body.

Stokes' law explains why the speed of a raindrop is less than a freely falling body with constant velocity, from the height of clouds.

The same law helps a man coming down with the help of a parachute, to slow down.

Terminal velocity refers to the constant velocity, acquired by a freely falling body in a viscous medium. Consider a small spherical body, falling freely due to gravity in a viscous medium.

The various forces acting on the body are:

• Weight of the body, acting downwards

• Viscous drag F_{V ,} acting upwards (opposing motion of the body)

• Upthrust or Buoyant force (F_T ) of liquids, equal to weight of the displaced liquid.

As the body falls, its velocity and the viscous drag increase due to gravity. There comes a stage, when all the three forces balance each other i.e. the net forces acting on the sphere is zero. When these conditions are achieved, the body starts moving with a constant velocity. This constant velocity is called as the terminal velocity.

Weight of the body =mg

where r is the radius of the body, r is density, g is the gravity due to upward viscous drag F_v = 6 ph vr (Stokes' law).

Note that if r s. the body moves up with constant velocity. For example, gas bubbles rise up through soda water bottle.