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MMLU-Pro / 9810 / A student is experimenting with a simple spring-block oscillator of spring…

Problem

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

question

A student is experimenting with a simple spring-block oscillator of spring constant k and amplitude A. The block attached to the spring has a mass of m. If the student places a small block of mass m on top of the original block, which of the following is true?

category

physics

options

  1. The small block is most likely to slide off when the original block is at maximum displacement from the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is less than kA/[(M+m)g].
  2. The small block is most likely to slide off when the original block is at the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than (M+m)g/(kA).
  3. The small block is most likely to slide off when the original block is at maximum displacement from the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than (M+m)g/(kA).
  4. The small block is most likely to slide off when the original block is at the equilibrium position, but will not slide off as long as the coefficient of kinetic friction between the blocks is greater than (M+m)g/(kA).
  5. The small block is most likely to slide off when the original block is at the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than kA/[(M+m)g].
  6. The small block is most likely to slide off when the original block is at maximum velocity, but will not slide off as long as the coefficient of static friction between the blocks is greater than kA/[(M+m)g].
  7. The small block is most likely to slide off when the original block is at maximum velocity, but will not slide off as long as the coefficient of static friction between the blocks is less than (M+m)g/(kA).
  8. The small block is most likely to slide off when the original block is at the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than (M+m)g/(2kA).
  9. The small block will not slide off regardless of the position of the original block as long as the coefficient of static friction between the blocks is greater than kA/[(M+m)g].
  10. The small block is most likely to slide off when the original block is at maximum displacement from the equilibrium position, but will not slide off as long as the coefficient of static friction between the blocks is greater than kA/[(M+m)g].

src

ori_mmlu-high_school_physics

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Source and history

upstream_id / Original problem ID
9810
task_id
a78276f6-d400-5b1c-8b08-ce9e501eb6c6
task_key
default--test--9810
task_revision_id
1
config / split
default / test

Official source

initial import