physics question about normal reaction plz help me out

3 solid hemispheres, each of radius (R) are placed in contact with each other, side by side, such that their flat surfaces rest on the rough horizontal ground . a solid sphere of mass(m) is symmetrically placed on the top of the three hemispheres . find the normal reaction between the solid sphere and any of the three hemispheres, assuming the system to be in stable equilibrium .

1 Answers

Divyaspandan ·

Since they are all symmetric, the normal reactions will be the samelet the normal reactions through the point of contact between a hemisphere and the sphere be NThen the vertical component of all the three normal reactions will balance out the weight of the sphere⇒ 3Nsin 60° = Mg⇒ 3N × √3/2 = Mg⇒ N = 2Mg/3√3or N =

2√3 Mg/9

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