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Two particles of mass m1 and m2 (m1 > m2) attract each other with a force inversely proportional to the square of the distance between them. If the particles are initially held at rest and then released, the centre of mass will
- a)move towards m1
- b)move towards m2
- c)remain at rest
- d)Nothing can be said
Correct answer is option 'C'. Can you explain this answer?
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Two particles of mass m1 and m2 (m1 > m2) attract each other with a f...
The centre of mass remains at rest because force of attraction is mutual. No external force is acting.
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Two particles of mass m1 and m2 (m1 > m2) attract each other with a f...
Explanation:
When two particles of mass m1 and m2 (m1 > m2) attract each other with a force inversely proportional to the square of the distance between them, we can analyze the motion of the system using the concept of the center of mass.
Center of Mass:
The center of mass of a system of particles is the point that behaves as if the entire mass of the system is concentrated at that point. It is the weighted average position of all the particles, taking into account their masses.
Initial Conditions:
In the given scenario, the two particles are initially held at rest. This means that the system is in equilibrium, and the center of mass of the system is at rest.
Force of Attraction:
The force of attraction between the two particles is inversely proportional to the square of the distance between them. This means that as the distance between the particles decreases, the force of attraction increases.
Motion of the Particles:
When the particles are released, they start moving towards each other due to the force of attraction between them. However, the motion of the particles depends on their masses.
Since m1 > m2, the particle with mass m1 experiences a greater force of attraction towards the particle with mass m2. As a result, the particle with mass m1 accelerates more than the particle with mass m2.
Motion of the Center of Mass:
The center of mass of the system is determined by the masses and positions of the particles. In this case, since m1 > m2, the particle with mass m1 has a greater influence on the position of the center of mass.
As the particle with mass m1 accelerates more, it covers a greater distance in the same time compared to the particle with mass m2. This causes the center of mass to move towards the particle with mass m1.
Conclusion:
Therefore, the center of mass of the system will move towards the particle with mass m1. It will not remain at rest, move towards m2, or exhibit any other behavior. Hence, the correct answer is option 'C' - the center of mass will remain at rest.
When two particles of mass m1 and m2 (m1 > m2) attract each other with a force inversely proportional to the square of the distance between them, we can analyze the motion of the system using the concept of the center of mass.
Center of Mass:
The center of mass of a system of particles is the point that behaves as if the entire mass of the system is concentrated at that point. It is the weighted average position of all the particles, taking into account their masses.
Initial Conditions:
In the given scenario, the two particles are initially held at rest. This means that the system is in equilibrium, and the center of mass of the system is at rest.
Force of Attraction:
The force of attraction between the two particles is inversely proportional to the square of the distance between them. This means that as the distance between the particles decreases, the force of attraction increases.
Motion of the Particles:
When the particles are released, they start moving towards each other due to the force of attraction between them. However, the motion of the particles depends on their masses.
Since m1 > m2, the particle with mass m1 experiences a greater force of attraction towards the particle with mass m2. As a result, the particle with mass m1 accelerates more than the particle with mass m2.
Motion of the Center of Mass:
The center of mass of the system is determined by the masses and positions of the particles. In this case, since m1 > m2, the particle with mass m1 has a greater influence on the position of the center of mass.
As the particle with mass m1 accelerates more, it covers a greater distance in the same time compared to the particle with mass m2. This causes the center of mass to move towards the particle with mass m1.
Conclusion:
Therefore, the center of mass of the system will move towards the particle with mass m1. It will not remain at rest, move towards m2, or exhibit any other behavior. Hence, the correct answer is option 'C' - the center of mass will remain at rest.
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Two particles of mass m1 and m2 (m1 > m2) attract each other with a force inversely proportional to the square of the distance between them. If the particles are initially held at rest and then released, the centre of mass willa)move towards m1b)move towards m2c)remain at restd)Nothing can be saidCorrect answer is option 'C'. Can you explain this answer?
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