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Question #77930

Difficulty: 5/10 | 🟢 Free

The Question

A spherical particle of radius $r = 1.00 \times 10^{-3} \text{ m}$ falls at a constant terminal velocity $v_t$ through a viscous liquid. The measured weight of the particle is $W = 3.56 \times 10^{-3} \text{ N}$ and the measured buoyant force exerted by the liquid is $F_b = 1.4 \times 10^{-3} \text{ N}$ . The dynamic viscosity of the liquid is $\eta = 0.796 \text{ Pa}\cdot\text{s}$ . Assuming Stokes' law is valid and treating $\pi$ as an exact number, what is the terminal velocity $v_t$ of the particle, expressed with the correct number of significant figures?

Options

A.
$0.15 \text{ m/s}$
B.
$0.144 \text{ m/s}$
C.
$0.14 \text{ m/s}$
D.
$0.147 \text{ m/s}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Significant Figures in Mixed Operations|Viscosity and Stokes' Law

Why This Question Is Tricky

Examiner Levers

Dimensional Analysis

Tests if the student verifies units/dimensions before selecting.

Difficulty Boost : +2

Common Mistakes

This question tests the student's ability to correctly apply the hierarchy of significant figure rules across mixed operations (addition/subtraction followed by multiplication/division) in a physical context.

Students commonly fall into the trap of treating the entire terminal velocity equation as a single continuous calculation, failing to round the intermediate force subtraction.

If they subtract $3.56 - 1.4 = 2.16$ and carry $2.16$ (which they incorrectly assume has 3 sig figs) into the division, they arrive at $0.144 \text{ m/s}$ or $0.14 \text{ m/s}$ .

By forcing the intermediate rounding via the decimal-place rule for subtraction, the net force drops to 2 significant figures ( $2.2$ ), which then dictates the precision of the final division, yielding $0.15 \text{ m/s}$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Units and Measurements - Class 11 Part 1
Concept	Significant Figures in Mixed Operations
Difficulty	5
Cognitive Load	6
Target Solve Time	140 sec
Access	Free