Derivation of centre of mass of two particle system.
Answers
Answered by
18
The centre of mass (CoM) is the point relative to the system of particles in an object. This is that point of the system of particles that embarks the average position of the system in relation to the mass of the object. At the centre of mass, the weighted mass gives a sum equal to zero. It is the point where any uniform force applied on the object acts.
In other words, a particle’s centre of mass is the point where Newton’s law of motions applies perfectly. When force is applied to the centre of mass, the object as a system of particles moves in the direction of force without rotating. No matter what the shape of the object, the centre of mass helps understand the mechanism of force and motion of that object.
Centre of Mass for Two Particles
For a system of two particles with equal masses, CoM is the point that lies exactly in the middle of both.

In the figure above, we take two particles with masses m1 and m2respectively lying on the x-axis. The distance of both the particles from the centre O is d1 and d2respectively. The CoM of this two system of particles is at point C lying at a distance D from point O. In this system of two particles D can be written as:
D = m1d1 + m2d2 / m1 + m2
From the equation D, can be taken as the mass-weighted mean of d1 and d2. Now, let us presume that the particles in the system have equal masses. Hence, m1=m2 = m, in this case,
D = (md1 + md2)/ 2m = m (d1 + d2) / 2m
D = (d1 + d2) / 2
From the equation above we get the centre of mass of two particles with equal masses. From the above equation, it is clear that the CoM of two particles lies in the midway of both.
Centre of Mass for n Particles
For a system of n particles, the centre of mass, according to its definition is:
D = m1d1 + m2d2 + m3d3 +…… mndn / m1 + m2 + m3 +….. mnm = ∑midi / mi
mi here is the sum of the masses of the particles.
In other words, a particle’s centre of mass is the point where Newton’s law of motions applies perfectly. When force is applied to the centre of mass, the object as a system of particles moves in the direction of force without rotating. No matter what the shape of the object, the centre of mass helps understand the mechanism of force and motion of that object.
Centre of Mass for Two Particles
For a system of two particles with equal masses, CoM is the point that lies exactly in the middle of both.

In the figure above, we take two particles with masses m1 and m2respectively lying on the x-axis. The distance of both the particles from the centre O is d1 and d2respectively. The CoM of this two system of particles is at point C lying at a distance D from point O. In this system of two particles D can be written as:
D = m1d1 + m2d2 / m1 + m2
From the equation D, can be taken as the mass-weighted mean of d1 and d2. Now, let us presume that the particles in the system have equal masses. Hence, m1=m2 = m, in this case,
D = (md1 + md2)/ 2m = m (d1 + d2) / 2m
D = (d1 + d2) / 2
From the equation above we get the centre of mass of two particles with equal masses. From the above equation, it is clear that the CoM of two particles lies in the midway of both.
Centre of Mass for n Particles
For a system of n particles, the centre of mass, according to its definition is:
D = m1d1 + m2d2 + m3d3 +…… mndn / m1 + m2 + m3 +….. mnm = ∑midi / mi
mi here is the sum of the masses of the particles.
harshitadebu:
plz mark as brainliest
thanku
plz Mark me na ....
Answered by
2
Answer:
yoUr ans is abOve so plz follow aNd mark my ANs as braiNnest pLz
Attachments:
Similar questions