Three solid hemispheres of radii R each are placed in contact with each other, with their flat faces on a rough horizontal surface. A sphere of mass M and radius R is placed symmetrically on top of th

Question

Three solid hemispheres of radii R each are placed in contact with each other, with their flat faces on a rough horizontal surface. A sphere of mass M and radius R is placed symmetrically on top of them. The normal reaction between the top sphere and any hemisphere, assuming the system to be static, is

TestHub · Accepted Answer

​ cos θ = AC AB ​ = a 3 2 ​ × 2 3 ​ ​ a ​ cos θ = 3 ​ 1 ​ 3 N sin θ = mg 3 N 3 ​ 2 ​ ​ = mg ∴ N = 3 2 ​ 3 ​ mg ​ = 6 ​ mg ​ Ans. ​

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