First slide

Viscous flow/Laminar flow

Question

A sphere of brass released in a long liquid column attains a terminal speed v₀. If the terminal speed is attained by a sphere of marble of the same radius and released
in the same liquid is nv₀, then the value of n will be
(Given: The specific gravities of brass, marble and liquid are 8.5 , 2.5 and 0.8 respectively)

Moderate

A

$\frac{5}{17}$
B

$\frac{17}{77}$
C

$\frac{11}{31}$
D

$\frac{17}{5}$

Solution

For the same radius, terminal velocity is proportional to the density difference.
$S o, \Rightarrow v_{o} \propto (8.5 - 0.8) a n d \Rightarrow n v_{o} \propto (2.5 - 0.8) D i v i d i n g w e g e t, \Rightarrow \frac{1}{n} = \frac{7.7}{1.7} \Rightarrow n = \frac{17}{77}$

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