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MMLU-Pro / 9485 / The volume charge density of a solid nonconducting sphere of radius …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

The volume charge density of a solid nonconducting sphere of radius $R=5.60 \mathrm{~cm}$ varies with radial distance rr as given by ρ=\rho= (14.1pC/m3)r/R\left(14.1 \mathrm{pC} / \mathrm{m}^3\right) r / R. What is the sphere's total charge?
Plain-text mathematical notation (without MathML)
The volume charge density of a solid nonconducting sphere of radius $R=5.60 \mathrm{~cm}$ varies with radial distance r as given by ρ= (14.1pC/m³)r/R. What is the sphere's total charge?
Original LaTeX notation
The volume charge density of a solid nonconducting sphere of radius $R=5.60 \mathrm{~cm}$ varies with radial distance $r$ as given by $\rho=$ $\left(14.1 \mathrm{pC} / \mathrm{m}^3\right) r / R$. What is the sphere's total charge?

category

physics

options

  1. $8.20$$\mathrm{fC}$
  2. $11.89\mathrm{fC}$
  3. $10.47\mathrm{fC}$
  4. $12.56\mathrm{fC}$
  5. $4.22\mathrm{fC}$
  6. $7.78$$\mathrm{fC} $
  7. $5.62$$\mathrm{fC}$
  8. $9.34$$\mathrm{fC}$
  9. $3.14\mathrm{fC}$
  10. $6.50\mathrm{fC}$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
9485
task_id
b8921daa-d322-5640-8e44-cab294921021
task_key
default--test--9485
task_revision_id
1
config / split
default / test

Official source

initial import