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Question #42003

Difficulty: 8/10 | 🟢 Free

The Question

A spherical particle falls through a viscous liquid and reaches terminal velocity. The following measurements are recorded:

Weight of the particle: W=7.59×10−5 NW = 7.59 \times 10^{-5} \text{ N} Buoyant force on the particle: Fb=7.2×10−5 NF_b = 7.2 \times 10^{-5} \text{ N} Viscosity of the liquid: η=1.0×10−1 Pa⋅s\eta = 1.0 \times 10^{-1} \text{ Pa}\cdot\text{s} Radius of the particle: r=5.00π mmr = \frac{5.00}{\pi} \text{ mm}

Assuming Stokes' law is valid, calculate the terminal velocity of the particle, expressing the result with the correct number of significant figures.

Options

  • A.

    1×10−3 m/s1 \times 10^{-3} \text{ m/s}

  • B.

    1.3×10−3 m/s1.3 \times 10^{-3} \text{ m/s}

  • C.

    1.30×10−3 m/s1.30 \times 10^{-3} \text{ m/s}

  • D.

    1.0×10−3 m/s1.0 \times 10^{-3} \text{ m/s}

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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

Common Mistakes

This question tests the strict application of the order of operations in significant figure rules during mixed operations.

Students must first evaluate the net force by subtracting the buoyant force from the weight.

According to the addition/subtraction rule, the result (0.39×10−50.39 \times 10^{-5}) must be rounded to the least number of decimal places present in the inputs (7.2×10−57.2 \times 10^{-5} has one), yielding 0.4×10−50.4 \times 10^{-5} N.

This intermediate rounding critically reduces the precision of the net force to a single significant figure.

When subsequently dividing by the drag coefficient to find the terminal velocity, the multiplication/division rule dictates that the final answer must be restricted to one significant figure.

The primary trap is ignoring the intermediate rounding step, which leads students to incorrectly retain two significant figures (1.3×10−31.3 \times 10^{-3} m/s) based on the initial given values.

Quick Facts About This Question

Question Information

SubjectPhysics
ChapterUnits and Measurements - Class 11 Part 1
ConceptSignificant Figures in Mixed Operations
Difficulty8
Cognitive Load7
Target Solve Time160 sec
AccessFree