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Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision

Three particles with masses of 1.0 kg , 2.0 kg and 3.0 kg are situated at the corners A , B and C respectively of an equilateral triangle ABC having an edge of 1 m . Find the coordinates of the centre of mass of the system, taking A as the origin and B along the positive x -axis.

Options

  1. A( 7 12 m , 3 4 m )
  2. B( 1 2 m , 3 6 m )
  3. C( 5 12 m , 3 4 m )
  4. D( 7 12 m , 3 2 m )

Correct answer

A. ( 7 12 m , 3 4 m )

Step-by-step solution

Taking A as the origin and B along the positive x -axis, the coordinates of the vertices of the equilateral triangle of side 1 m are: A = (0, 0) B = (1, 0) C = (1 60^ , 1 60^ ) = ( 1 2 , 3 2 ) The masses at these points are m_A = 1.0 kg , m_B = 2.0 kg , and m_C = 3.0 kg . The x -coordinate of the centre of mass is given by: x_ cm = m_A x_A + m_B x_B + m_C x_C m_A + m_B + m_C x_ cm = 1.0(0) + 2.0(1) + 3.0 ( 1 2 ) 1.0 + 2.0 + 3.0 x_ cm = 0 + 2 + 1.5 6 = 3.5 6 = 7 12 m The y -coordinate of the centre of mass is given

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