The center of mass of three particles of masses 1 kg, 2 kg and 3 kg at (3, 3, 3) with reference to a fixed coordinate system. Where should a fourth particle of mass 4 kg should be placed, so that the center of mass of the system of all particles shifts to a point (1, 1, 1)?

The center of mass of three particles of masses 1 kg, 2 kg and 3 kg at (3, 3, 3) with reference to a fixed coordinate system. Where should a fourth particle of mass 4 kg should be placed, so that the center of mass of the system of all particles shifts to a point (1, 1, 1)?

a)

(-1, -1, -1)

b)

(-2, -2, -2)

c)

(2, 2, 2)

d)

(1, 1, 1)

1 Answer

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Answer Key / Explanation : (b) -

(b)

Centre of Mass of a solid body is given by

…(i)

and

(given)

…(ii)

Solving Eqs. (i) and (ii), we get

Similarly,

The fourth particle must be placed at the point (-2, -2, -2).