SATHEE: Physics And Measurement Question 259

Physics And Measurement Question 259

Question: When a small sphere moves at low speed through a fluid, the viscous force F, opposing the motion is experimentally found to depend upon the radius r, the velocity v of the sphere and the viscosity $η$ of the fluid. Expression for force is

Options:

A) $4 π η r v^{2}$

B) $4 π η r^{2} v$

C) $2 π η r^{2} v$

D) $6 π η r v$

Show Answer

Answer:

Correct Answer: D

Solution:

[d] We can thus say that the viscous force (F) is the function of radius (r), velocity (v) and viscosity ( $η$ ). $o r F = f (η, r, v) o r F = k η^{x} r^{y} v^{z}$ …… (1)

Where k is a constant. Now, dimensions of the constituents are
$∴ [M L T^{- 2}] = {[M L^{- 1} T^{- 1}]}^{x} {[L]}^{y} {[L T^{- 1}]}^{z}$

$= [M^{x} L^{- x + y + z} T^{- x - z}]$

Equating the exponents of similar quantities of both sides we get, $x = 1; - x + y + z = 1$ and $- x - z = - 2$

Solving for $x, y & z,$ , we get $x = y = z = 1$ Equation (1) becomes $F = k η r v$

Experimentally, it was found that $k = 6 π o r F = 6 π η r v$ , which is the famous Stokes’ law.

Physics And Measurement Question 259

Question: When a small sphere moves at low speed through a fluid, the viscous force F, opposing the motion is experimentally found to depend upon the radius r, the velocity v of the sphere and the viscosity $η$ of the fluid. Expression for force is

Options:

Answer:

Solution:

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Physics And Measurement Question 259

Question: When a small sphere moves at low speed through a fluid, the viscous force F, opposing the motion is experimentally found to depend upon the radius r, the velocity v of the sphere and the viscosity η of the fluid. Expression for force is

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: When a small sphere moves at low speed through a fluid, the viscous force F, opposing the motion is experimentally found to depend upon the radius r, the velocity v of the sphere and the viscosity $η$ of the fluid. Expression for force is