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

As illustrated in the figure, a water molecule has a specific structure. Determine the distance of the molecule's centre of mass from the centre of the oxygen atom.

Options

  1. A3.3 10⁻¹² m
  2. B8.4 10⁻¹² m
  3. C7.4 10⁻¹² m
  4. D6.6 10⁻¹² m

Correct answer

D. 6.6 10⁻¹² m

Step-by-step solution

Let the oxygen atom be at the origin (0,0) . The y-axis is taken along the bisector of the H-O-H angle. The angle of each O-H bond with the y-axis is = 104^ 2 = 52^ . The coordinates of the two hydrogen atoms are (d 52^ , -d 52^ ) and (-d 52^ , -d 52^ ) , where d = 0.96 10⁻¹⁰ m . Mass of oxygen atom, m_O = 16 u Mass of hydrogen atom, m_H = 1 u By symmetry, the x-coordinate of the centre of mass is 0 . The y-coordinate of the centre of mass is: y_ cm = m_O y_O + m_H y_ H₁ + m_H y_ H₂ m_O + 2m_H y_ cm = 16(0) + 1(-d

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