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The centre of mass of two particles lies
- a)on the line perpendicular to the line joining the particles
- b)on a point outside the line joining the particles
- c)on the line joining the particles.
- d)none of the above
Correct answer is option 'C'. Can you explain this answer?
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The center of mass of a system of particles is the point at which the entire mass of the system can be considered to be concentrated. It is a point that simplifies the analysis of the system's motion. The position of the center of mass depends on the distribution of masses within the system.
The center of mass of two particles can be determined by considering the concept of weighted average. The position of each particle is weighted by its mass, and the center of mass is calculated as the average of these positions.
Let's consider two particles with masses m1 and m2, located at positions r1 and r2, respectively.
1. The Line Joining the Particles:
The center of mass of a system of two particles always lies on the line joining the particles. This is because the position of each particle is weighted by its mass, and the center of mass is calculated as the average of these positions. Since the position of each particle is multiplied by its mass, the center of mass will be closer to the particle with greater mass. Therefore, the center of mass will lie on the line joining the particles.
2. Perpendicular Line:
The center of mass does not lie on a line perpendicular to the line joining the particles. If the center of mass were to lie on a line perpendicular to the line joining the particles, it would indicate that the center of mass is equidistant from both particles. However, since the position of each particle is weighted by its mass, the center of mass will be closer to the particle with greater mass. Therefore, it will not be equidistant from both particles, and hence will not lie on a line perpendicular to the line joining the particles.
3. Point Outside the Line Joining the Particles:
The center of mass does not lie outside the line joining the particles. As mentioned earlier, the center of mass is calculated as the average of the positions of the particles, weighted by their masses. This means that the center of mass will always lie between the two particles, closer to the particle with greater mass. Therefore, it will not lie outside the line joining the particles.
In conclusion, the correct answer is option C - the center of mass of two particles lies on the line joining the particles.
The center of mass of two particles can be determined by considering the concept of weighted average. The position of each particle is weighted by its mass, and the center of mass is calculated as the average of these positions.
Let's consider two particles with masses m1 and m2, located at positions r1 and r2, respectively.
1. The Line Joining the Particles:
The center of mass of a system of two particles always lies on the line joining the particles. This is because the position of each particle is weighted by its mass, and the center of mass is calculated as the average of these positions. Since the position of each particle is multiplied by its mass, the center of mass will be closer to the particle with greater mass. Therefore, the center of mass will lie on the line joining the particles.
2. Perpendicular Line:
The center of mass does not lie on a line perpendicular to the line joining the particles. If the center of mass were to lie on a line perpendicular to the line joining the particles, it would indicate that the center of mass is equidistant from both particles. However, since the position of each particle is weighted by its mass, the center of mass will be closer to the particle with greater mass. Therefore, it will not be equidistant from both particles, and hence will not lie on a line perpendicular to the line joining the particles.
3. Point Outside the Line Joining the Particles:
The center of mass does not lie outside the line joining the particles. As mentioned earlier, the center of mass is calculated as the average of the positions of the particles, weighted by their masses. This means that the center of mass will always lie between the two particles, closer to the particle with greater mass. Therefore, it will not lie outside the line joining the particles.
In conclusion, the correct answer is option C - the center of mass of two particles lies on the line joining the particles.
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