Question

Consider a small sphere of mass $m$ dropped from a greater height. It attains terminal speed after it falls through $200m$ and will continue to fall at that speed. The work done by air friction on sphere during first $200m$ fall is

• A. greater than the work done by air friction in the second $200m$
• B. lesser than the work done by air friction in the second $200m$
• C. equal to the work done by air friction in the second $200m$
• D. given data is insufficient.

Answer 1

The correct option is B lesser than the work done by air friction in the second $200m$

When the sphere falls through first $200m$, the viscous force acting on it increases in value from zero to $(F_v{)}_{max}=6\pi \eta r(v_T)$
However, during next $200m$ fall, this viscous force remains constant at $(F_v{)}_{max}$.
Clearly, work done by air friction in second part is more.