In which of the following cases, a force will not be required to keep the particle in the given motion?

Question

Accepted Answer

1. **Newton's Second Law:** The net external force acting on a particle is equal to the rate of change of its linear momentum ($ec{F} = rac{dec{p}}{dt}$) [Source 57, 69].
2. **Condition for No Force:** For a force not to be required ($ec{F} = 0$), the rate of change of momentum must be zero. This implies that the momentum $ec{p}$ must be constant ($ec{p} = 	ext{constant}$).
3. **Analyze Options:**
   - **Circular Motion:** The direction of velocity changes continuously, meaning momentum changes. This requires a centripetal force [Source 66].
   - **Straight Line:** A particle can move in a straight line with changing speed (acceleration). If it accelerates, force is required ($F=ma$).
   - **Constant Acceleration:** A constant non-zero acceleration implies a constant non-zero force ($F=ma$) [Source 55].
   - **Constant Momentum:** This satisfies the condition $ec{F} = 0$ directly.

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