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MHT CET202617 April 2026Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Three identical spheres, each of mass 'm' kg, are kept as shown in the figure, touching each other, with their centers on a straight line. If their centers are marked as A, B, C respectively, the distance of center of mass of the system from A is

Options

  1. AAB+BC 3
  2. BAB+AC 3
  3. CAC+BC 2
  4. DAB+BC+AC 3

Correct answer

B. AB+AC 3

Step-by-step solution

Let the mass of each sphere be m . Let the center of sphere A be at the origin (0,0) . The coordinates of the centers of the three spheres along the X-axis are: x_A = 0 x_B = AB x_C = AC The distance of the center of mass of the system from A (the origin) is given by the formula: x_ cm = m x_A + m x_B + m x_C m + m + m Substituting the coordinates into the equation: x_ cm = m(0) + m(AB) + m(AC) 3m x_ cm = AB + AC 3 Answer: AB+AC 3

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