Question

Two small spheres of radii $r$ and $3 r$ fall through a viscous liquid with the same constant speed. The viscous forces experienced by them are in the ratio: (a) $1: 4$ (b) $1: 2$ (c) $1: 3$ (d) $3: 1$

Name: Problem 42, Chapter 7: Objective Physics : NEET 2020 Examination textbook Gurukul Oswal
Uploaded: 2021-10-06T04:24:35-08:00
Duration: 1 min 16 s
Channel: Suman Saurav Thakur
Description: Two small spheres of radii r and 3 r fall through a viscous liquid with the same constant speed. The viscous forces experienced by them are in the ratio: (a) 1: 4 (b) 1: 2 (c) 1: 3 (d) 3: 1

   Two small spheres of radii $r$ and $3 r$ fall through a viscous liquid with the same constant speed. The viscous forces experienced by them are in the ratio:
(a) $1: 4$
(b) $1: 2$
(c) $1: 3$
(d) $3: 1$

Objective Physics : NEET 2020 Examination textbook Gurukul Oswal

Gurukul Oswal… 2020 Edition

Chapter 7, Problem 42

Instant Answer

Solved by Expert Suman Saurav Thakur

10/06/2021

Step 1

Step 1: According to Stokes' law, the viscous force experienced by a sphere moving through a viscous fluid is given by the formula $F = 6\pi\eta rv$, where $\eta$ is the coefficient of viscosity of the fluid, $r$ is the radius of the sphere, and $v$ is the velocity Show more…

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Two small spheres of radii $r$ and $3 r$ fall through a viscous liquid with the same constant speed. The viscous forces experienced by them are in the ratio: (a) $1: 4$ (b) $1: 2$ (c) $1: 3$ (d) $3: 1$

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Key Concepts

Stokes’ Law

Stokes’ Law gives the expression for the viscous drag force experienced by a sphere moving through a viscous fluid at low Reynolds numbers. The law states that the drag force is proportional to the fluid’s viscosity, the sphere’s radius, and its velocity, making it crucial for analyzing motion in such conditions.

Direct Proportionality to Radius

For spheres moving at the same constant speed in a viscous liquid, the drag force is directly proportional to the sphere's radius. This means that if one sphere has a radius that is a multiple of the other, its viscous force will be scaled by that same multiple, leading to the ratio of forces being equal to the ratio of their radii.

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