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MMLU-Pro / 10272 / In an elastic collision of two particles with masses m₁ and m₂, the…

Problem

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

question

In an elastic collision of two particles with masses m1m_1 and m2m_2, the initial velocities are u1\mathbf{u}_1 and u2=αu1\mathbf{u}_2=\alpha \mathbf{u}_1. If the initial kinetic energies of the two particles are equal, find the conditions on u1/u2u_1 / u_2 such that m1m_1 is at rest after the collision and α\alpha is positive.
Plain-text mathematical notation (without MathML)
In an elastic collision of two particles with masses m₁ and m₂, the initial velocities are u₁ and u₂=αu₁. If the initial kinetic energies of the two particles are equal, find the conditions on u₁/u₂ such that m₁ is at rest after the collision and α is positive.
Original LaTeX notation
In an elastic collision of two particles with masses $m_1$ and $m_2$, the initial velocities are $\mathbf{u}_1$ and $\mathbf{u}_2=\alpha \mathbf{u}_1$. If the initial kinetic energies of the two particles are equal, find the conditions on $u_1 / u_2$ such that $m_1$ is at rest after the collision and $\alpha$ is positive.

category

physics

options

  1. $5 \pm 2 \sqrt{3}$
  2. $3 \pm 2 \sqrt{2}$
  3. $2 \pm \sqrt{3}$
  4. $2 \pm \sqrt{2}$
  5. $4 \pm 2 \sqrt{3}$
  6. $4 \pm \sqrt{2}$
  7. $1 \pm \sqrt{3}$
  8. $1 \pm \sqrt{2}$
  9. $3 \pm \sqrt{5}$
  10. $6 \pm 2 \sqrt{5}$

src

scibench-class

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Source and history

upstream_id / Original problem ID
10272
task_id
b433eb33-62b3-5320-8fac-7b0eb93ac2b0
task_key
default--test--10272
task_revision_id
1
config / split
default / test

Official source

initial import