Question

A sphere of brass released in a long liquid column attains a terminal speed $v_{0}$. If the terminal speed attained by sphere of marble of the same radius and released in the same liquid is $n v_{0}$, then the value of $n$ will be (Given: The specific gravities of brass, marble and the liquid are $8.5 , 2.5 $ and $0.8$ respectively.)

• A. $\frac{5}{17}$
• B. $\frac{17}{77}$
• C. $\frac{11}{31}$
• D. $\frac{17}{5}$

Answer 1

Answer: (B)

$v_{C}=\frac{2}{9} r^{2} \frac{\left(\rho-\rho^{\prime}\right) g}{\eta}$
Here, $\frac{n v_{0}}{v_{0}}=\frac{\rho_{\text {marble }}-\rho_{\text {liquid }}}{\rho_{\text {brass }}-\rho_{\text {liquid }}}=\frac{2.5-0.8}{8.5-0.8}=\frac{1.7}{7.7}$
or $n=\frac{17}{77}$