Question

A solid sphere falls with a terminal velocity of $20{\text{ms}}^{-1}$ in air. If it is allowed to fall in vacuum.

• A. Terminal velocity will be $20{\text{ms}}^{-1}$
• B. Teminal velocity will be less than $20{\text{ms}}^{-1}$
• C. Terminal velocity will be greater than $20{\text{ms}}^{-1}$
• D. No terminal velocity will be attained

Answer 1

The correct option is D No terminal velocity will be attained

We know that,
Terminal velocity of a sphere falling through a medium is given by
$v=\frac{2\times r^2(\rho -\sigma )g}{9\eta }$
In vacuum, there is no resistive force (i.e) no viscosity $\therefore$ $\eta =0$
When $\eta =0$, terminal velocity is infinity.
Hence, we can conclude that terminal velocity can not be acquired by the sphere falling through the vacuum..