Q 11-09-079JEE MainJEE Main 2024 (31 Jan, Shift 2)Medium
A small spherical ball of radius $r$, falling through a viscous medium of negligible density, has terminal velocity $v$. Another ball of the same mass but of radius $2r$, falling through the same viscous medium, will have terminal velocity:
Answer: (A) $\dfrac v2$
With negligible buoyancy, at terminal velocity $mg = 6\pi\eta rv$, so $v = \dfrac{mg}{6\pi\eta r} \propto \dfrac1r$ for the same mass.
Doubling the radius halves the terminal velocity: $\dfrac v2$.
Solution by Sreeraj P, M.Sc Physics