Explain the concept of centre of mass.Obtain an expression for the position vector of centre of mass of n particle system
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student-name Krishna Kanth asked in Physics
obtain an expression for position vector of centre of mass of a two particle system
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student-name Shikha Bhadoria answered this
297 helpful votes in Physics, Class X
Centre of Mass of System of two Particles
Let us consider a system of two particles having mass m1 and m2. Let the distances of two particles be x1 and x2 respectively from some origin O.
The centre of mass of the system is that point C, which is at a distance X from O, where X is given by,
So, the position vector is:
If, the masses are placed in the plane such that m1 is at (x1,y1) and m2 is at (x2,y2).
This means the position vector of m1 and m2 is:
Then, by going on same lines as before we obtain X (as (i)) and Y.
In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration.
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