Question

Two steel marbles (ofradii Rand R/3) are released in a highly viscous liquid. The ratio of the terminal velocity of the larger marble to that of the smaller is. b] 3 c] 1 d] 1/9 a) 9​

Answer 1

Given:

Two steel marbles (of radii R and R/3) are released in a highly viscous liquid.

To find:

Ratio of the terminal velocity of the larger marble to that of the smaller marble?

Calculation:

Terminal Velocity equation is :

$\sf \: v_{t} = \dfrac{2}{9} {r}^{2} g \bigg( \dfrac{ \rho - \sigma}{ \eta} \bigg)$

For constant density, viscosity, we can say :

$\sf \: v_{t} \propto {r}^{2}$

Now, taking necessary ratios :

$\rm\: \dfrac{v_{large}}{v_{small}} = \dfrac{ {R}^{2} }{ {( \frac{R}{3} )}^{2} }$

$\rm \implies\: \dfrac{v_{large}}{v_{small}} = 9$

So, required ratio is 9.