Question

A solid sphere, of radius R acquires a terminal velocity v₁ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity η. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, ν₂, when falling through the same fluid, the ratio (v₁/v₂) equals :
(A) 27 (B) 1/27
(C) 9 (D) 1/9

Answer 1

Answer:

hey mate

Explanation:

maybe

c) 1/9

hope will be right

Answer 2

v₁/v₂ = 9:1

Hence option C is correct

•According to stoke's law terminal velocity V = 2gr²(p. - p)/9η

where

g is acceleration due to gravity

r = radius of object

η = viscosity coefficient

•If a solid sphere is broken into 27 sphere

•then, let the radius of new sphere is r

=> 4πR³/3 = 27 × 4πr³/3

=> R³ = 27r

=> R = 3r

•Terminal velocity

v₁ = 2gR²(p.- p)/9η

___________(1)

•Terminal velocity

ν₂ = 2gr²(p.- p)/9η

Putting r = R/3

Terminal velocity

ν₂ = 2gR²(p.- p)/81η

__________(2)

•dividing (1)&(2)

v₁/v₂ = 9:1

• Hence option C is correct.