The centre of mass of a system of two particles of masses m1 and m2 is at a distance d1 from m1

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Q10

Centre of mass of three particles of masses 1 kg, 2kg 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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Text Solution

`d_1/d_2 = m_2/m_1``d_1/d_2 = m_1/m_2``d_1/d_2 = m_1/m_1 + m_2``d_1/d_2 = m_2/m_1 + m_2`

Answer : A

Solution : Refer figure, <br> The distance of center of mass CM from masses `m_(1)` and `m_(2)` are <br> `d_(1)=(m_(2)d)/(m_(1)+m_(2))` and `d_(2)=(m_(1)d)/(m_(1)+m_(2))` `therefore d_(1)/d_(2)=m_(2)/m_(1)` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NCERT_OBJ_FING_PHY_XI_C07_E01_007_S01.png" width="80%">