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

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Solution

Q.
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 $2 r$ , falling through the same viscous medium will have terminal velocity [2024]

1 $v / 2$

2 $v / 4$

3 $4 v$

4 $2 v$

Ans.
(1)

Since density is negligible hence Buoyancy force will be negligible

  At terminal velocity,

   $M g = 6 π η r v$

$v \propto \frac{1}{r}$ (as mass is constant)

Now, $\frac{v}{v^{'}} = \frac{r^{'}}{r}$

   $r^{'} = 2 r$

So, $v^{'} = \frac{v}{2}$

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