devarshi-dt-logo

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 v2 when falling through the same fluid, the ratio (v1/v2) equals:

27

1/9

1/27

9

Solution:

Correct option is D. 9
We have VT = (2/9)r²η(ρ₀ - ρl)g => vT ∝ r²
Since mass of the sphere will be same
ρ(4/3)πR³ = 27.(4/3)πr³ρ => r = R/3
∴v1/v2 = R²/r² = 9