Question

Derive an expression for center of mass of 3 particle system

Answer 1

Explanation:

Complex objects have particles that show mechanism differently. When we work on a system of particles we need to know its centre of mass to calculate the mechanics of oddly shaped objects. Rigid bodies constitute a system of particles which govern its motion and equilibrium. With the Centre of Mass, we can effortlessly understand the mechanism of complicated objects.

Answer 2

Center of mass of 3 particle system is $r=\frac{m_{1} r_{1}+m_{2} r_{2} +m_{3} r_{3}}{m_{1}+m_{2}+m_{3} }$

Explanation:

• Center of mass of any body or system is defined as the imaginary point where whole mass of the body or system is assumed to be concentrated and if we do any change in the system the change directly applied to the center of mass will be same
• It is also defined as the average position of the system related to its mass so it the point where whole mass of the system is contained and can be balanced at that point

• Given the system have 3 particles,

let three particles have masses m₁ , m₂ and m₃

and there distances from center of mass r₁ ,r₂ and r₃

let 'r' be the center of mass

As center of mass is the point where change occur is same as that on whole system

=> (m₁+ m₂ +m₃) r = m₁ r₁ + m₂r₂ +m₃r₃

=> r = $\frac{m_{1}r_{1} + m_{2}r_{2} +m_{3}r_{3} }{m_{1} +m_{2}+m_{3} }$

To know more about center of mass, visit:

Calculate the velocity of the center of mass of the system of particles shown in figure (9-E3).

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The centre of mass of a system of three particles of masses 1g, 2g and 3g is taken as the origin of a coordinate system. The position vector of a fourth particle of mass 4g such that the centre of mass of the four particle system lies at the point (1, 2, 3) is α(î + 2Ä + 3), where α is a constant. The value of α is :- (1)10/3(2)5/2(3)1/2(4)2/5

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