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Two smooth spheres, each of radius 5   cm and weight W , rest one over the other, inside a fixed smooth cylinder of radius 8   cm . The reactions between the spheres and the vertical side of the cylinder are

Options

  1. AW 4 and 3 W 4 .
  2. BW 4 and W 4 .
  3. C3 W 4 and 3 W 4 .
  4. DW and W .

Correct answer

C. 3 W 4 and 3 W 4 .

Step-by-step solution

The given case can be visualized through the figure shown below, Let A be the left sphere and B be the right sphere. The free body diagrams of A and B are, For the horizontal equilibrium of the system ( A and B ), let N AW and N BW be the normal reaction forces applied by the sidewalls of the cylinder on spheres A and B , respectively, N AW = N BW     … i From the diagrams, in triangle A B O , we have, cos θ = 6 10 ⇒ θ = 53 °     … ii From sphere B , ⇒ N AB

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