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GATE 2021 ME (ME1) – Question 60

Engineering Mechanics · Free-body diagrams and equilibrium · 2 marks · Numerical answer

Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm. The reaction at the point of contact between two spheres is _____ N (round off to one decimal place).

Two equal spheres of radius 125 mm touching each other and opposite walls of a 400 mm wide channel. See the attached source image.

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Correct answer: 124.38 to 125.62

Explanation

Centre-to-centre horizontal separation is 400−2(125)=150 mm. The distance between centres is 250 mm, so vertical separation is $\sqrt{250^2-150^2}=200$ mm.

The upper sphere’s weight is balanced by the contact force’s vertical component: R(200/250)=100. Therefore **R=125.0 N**.