Question

A uniform solid sphere of relative density $5$ is released in water filled in a long vertical tube. Its terminal velocity achieved is $V$. If another uniform solid sphere of the same material but double the radius is released in the same water, then the terminal velocity achieved will be

• A. $V\setminus 4$
  
• B. $4V$
• C. $V$
• D. $2V$

Answer 1

The correct option is B $4V$

We know that $F=6\pi \eta rv$
Initially the terminal velocity $V$ of sphere of radius $a$ is,
$W_{eff}=6\pi \eta aV$
$(W_{eff}$= weight-buoyant force)
As the radius is doubled, mass is increased to 8 times and new terminal velocity will be
$8W_{eff}=6\pi \eta 2a{V}^{\prime }$
From $\left(i\right)$ and $\left(ii\right)$,
$V^{\prime }=4V$
Final Answer: (b)