InterviewSolution
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InterviewSolution
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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 3 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 ?A. `(0, 0,0)`B. `(1, 3,2)`C. `(-1, 2,3)`D. `(3, 1, 8)` |
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Answer» Correct Answer - D (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 as `(x_3,y_3,z_3)` i.e., `m_1 = 6kg, (x_1,y_1,z_1) = (1,2,3)` `m_2 = 5 kg(x_2,y_2,z_2) = (-1, 3, - 2)` `m_1 = 5 kg(x_3,y_3, z_3) = (1,2,3)` Given, `(X_(CM), Y_(CM), Z_(CM) = (1,2,3)` Using `X_(CM) = (m_1 x_1 + m_2 x_2 + m_3 x_3)/(m_1 + m_2 + m_3)` `1 = (6 xx 1 + 5 xx(-1)+ 5x_3)/(6 + 5 + 5)` `5 x_3 = 16-1 = 15` or `x_3 = 3` Similarly, `y_3 = 1 and z_3 = 8`. |
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