Question

A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of earlier falling through the same viscous medium will have terminal velocity

• A. $v$
• B. $\frac{v}{4}$
• C. $\frac{v}{2}$
• D. $2v$

Answer 1

The correct option is C $\frac{v}{2}$

If $\rho$ is the density of the ball and ${\rho }^{\prime }$ that of the another ball, m for the balls are same, but $r^{\prime }=2r$ (the density of the liquid is neglected as it is not given otherwise the upward thrust will be different)
$\therefore mg=6\pi r\eta v=6\pi 2r\eta v^{\prime }$ by stoke's law $\Rightarrow v^{\prime }=\frac{v}{2}$.