Q123 / 170 · Manipal (MET) 2021 · Physics

A particle is moving in a circular path with a constant speed $v$. If $\theta$ is the angular displacement. Then starting from $\theta=0$, the maximum and minimum changes in the momentum will occur, when value of $\theta$ is respectively:

  • A
    $45^{\circ}$ and $90^{\circ}$
  • B
    $90^{\circ}$ and $180^{\circ}$
  • Correct answer
    C
    $180^{\circ}$ and $360^{\circ}$
  • D
    $90^{\circ}$ and $270^{\circ}$

Solution

When $\theta=180^{\circ}$, the particle will be at diametrically opposite point. Where its velocity is opposite to the direction of motion. The change in momentum $=m v-(-m v)+2 m v$ (maximum). When $\theta=360^{\circ}$, the particle is at the initial position with momentum $m v$ change in momentum $=m v-m v=0$ (minimum).

Hence, the correct answer is option: 'C'.

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