Q.

Centre of mass of three particles of masses 1 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?

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a

(0, 0, 0)

b

(1, 3, 2)

c

(-1, 2 , 3)

d

(3, 1, 8)

answer is D.

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Detailed Solution

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)m3=5 kg, let its position is (x3,y3.z3)Given, (XCM, YCM, ZCM) = (1, 2, 3)1 = 6×1+5×(-1)+5x36+5+55x3 = 16-1 = 15 or x3 = 3Similarly, y3 = 1 and z3 = 8
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