# Drag on the Sphere

A sphere of radius $$r$$ is abandoned in a chamber of height $$H$$ ($$H$$ much greater than $$r$$) filled with a fluid with viscosity $$\eta$$ and density $$\rho$$. According to the Stoke's Law, for small velocities and laminar flow, the frictional force exerted by the viscous fluid in the sphere is given by the expression $$\vec { { F }_{ d } } =-6\pi r\eta \vec { v }$$. If $$W$$ is the total work done by frictional force and buyoancy until the sphere reaches the height $$h$$ in which the resultant force is zero, the correct expression for $$h$$ is...

Details and Assumptions:

• Use $$m$$ for sphere's mass and $$g$$ for the gravitational acceleration.

• Assume also that the time elapsed is infinitely long, so that the sphere's velocity actually reaches the terminal velocity.

×