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MMLU-Pro / 9236 / In a spherical metal shell of radius R, an electron is shot from the center…

Problem

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

question

In a spherical metal shell of radius RR, an electron is shot from the center directly toward a tiny hole in the shell, through which it escapes. The shell is negatively charged with a surface charge density (charge per unit area) of 6.90×10−13C/m26.90 \times 10^{-13} \mathrm{C} / \mathrm{m}^2. What is the magnitude of the electron's acceleration when it reaches radial distances r=0.500Rr=0.500 R?
Plain-text mathematical notation (without MathML)
In a spherical metal shell of radius R, an electron is shot from the center directly toward a tiny hole in the shell, through which it escapes. The shell is negatively charged with a surface charge density (charge per unit area) of 6.90×10^(−13)C/m². What is the magnitude of the electron's acceleration when it reaches radial distances r=0.500R?
Original LaTeX notation
In a spherical metal shell of radius $R$, an electron is shot from the center directly toward a tiny hole in the shell, through which it escapes. The shell is negatively charged with a surface charge density (charge per unit area) of $6.90 \times 10^{-13} \mathrm{C} / \mathrm{m}^2$. What is the magnitude of the electron's acceleration when it reaches radial distances $r=0.500 R$?

category

physics

options

  1. $0$
  2. $2.0 \times 10^{15} \, \mathrm{m/s^2}$
  3. $5.5 \times 10^{15} \, \mathrm{m/s^2}$
  4. $3.0 \times 10^{15} \, \mathrm{m/s^2}$
  5. $7.5 \times 10^{14} \, \mathrm{m/s^2}$
  6. $2.5 \times 10^{15} \, \mathrm{m/s^2}$
  7. $1.5 \times 10^{15} \, \mathrm{m/s^2}$
  8. $6.0 \times 10^{15} \, \mathrm{m/s^2}$
  9. $9.0 \times 10^{14} \, \mathrm{m/s^2}$
  10. $4.5 \times 10^{15} \, \mathrm{m/s^2}$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
9236
task_id
75d4e84f-92e4-580f-802a-0775a32c44a2
task_key
default--test--9236
task_revision_id
1
config / split
default / test

Official source

initial import