Physics

Problem

In a certain experiment to measure the ratio of charge to mass of elementary particles, a surprising result was obtained in which two particles moved in such a way that the distance between them always remained constant. It was also noticed that this two-particle system was isolated from all other particles and no force was acting on this system except the force between these two masses. After careful observation followed by intensive calculation, it was deduced that velocity of these two particles was always opposite in direction and magnitude of velocity was

10^3 \text{ ms}^{-1}

and

2 \times 10^3 \text{ ms}^{-1}

for first and second particle, respectively, and masses of these particles were

2 \times 10^{-30} \text{ kg}

and

10^{-30} \text{ kg}

, respectively. Distance between them were

12 \text{ \AA}

(

1 \text{ \AA} = 10^{-10} \text{ m}

). Acceleration of the first particle was (1) zero (2)

4 \times 10^{16} \text{ ms}^{-2}

(3)

2 \times 10^{16} \text{ ms}^{-2}

(4)

2.5 \times 10^{15} \text{ ms}^{-2}

Intuitive explanation

This problem hinges on conservation of momentum in an isolated two-particle system. Since the particles maintain constant separation while moving with opposite velocities, they must be rotating about their common center of mass—think of it like a dumbbell spinning. The key insight is that momentum conservation requires the center of mass to remain stationary, which constrains the mass ratio and their accelerations. Use the fact that the net momentum must be zero to find what acceleration the first particle must have.

Intuitive explanation

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