Proportionality of Dimensions

Classical Mechanics Level 3

Two spheres of equal mass but radii $R$ and $2R$ are allowed to fall in a liquid. The ratio of their terminal velocities is?

1:32

2:1

1:4

1:2

2 solutions

Tanishq Varshney
Apr 6, 2015

Since they are spheres apply $F=6 \pi \eta r v_{d}$

how, 2:1,it should be 4:1, bcoz terminal velocity is directly proportional to square of its radius. reply fast

ALFRED MARSHALL - 6 years, 2 months ago

The above formula stated is applicable only for spheres.

Tanishq Varshney - 6 years, 2 months ago

so what is your question about?u have written spheres only.

ALFRED MARSHALL - 6 years, 2 months ago

STROKES LAW

Krishna Shankar - 6 years, 2 months ago

Lu Chee Ket
Nov 2, 2015

v = Sqrt [2 m g/ (C r A)] {Same mass but with different cross sectional areas Pi R^2 as projected areas.}

v1/ v2 = Sqrt [(Pi 4 R^2)/ (Pi R^2] = 2 : 1

https://en.wikipedia.org/wiki/Terminal_velocity