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Centre of mass of three particles of masses I kg, 2 kg and 3 kg lies at the point (1, 2, 3) and centre of mass of another system of particles 3 kg and 2 kg lies at the point (-1, 3, -2). Where should we put a particle of mass 5 kg so that the centre of mass of entire system lies at the centre of mass of first system?
detailed solution
Correct option is D
According to the definition of centre of mass, we can imagine one particle of mass (1 + 2 + 3) kg at (1,2, 3); another particle of mass (2 + 3) kg at (-1, 3,-2).Let the third particle of mass 5 kg put at (x3, y3, z3) i.e.m1 = 6 kg, (x1, y1,z1) = (1,2,3)m2 = 5 kg, (x2, y2,z2) = (-1, 3,-2)m1 = 5 kg, (x3, y3,z3) Given, (XCM, YCM, ZCM) = (1, 2, 3)Using XCM = m1x1+m2x2+m3x3m1+m2+m31 = 6×1+5×(-1)+5x36+5+55x3 = 16-1 = 15 or x3 = 3Similarly, y3 = 1 and z3 = 8Talk to our academic expert!
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