Question

Two equal heavy spheres, each of radius r, are in equilibrium within a smooth cup of radius 3r. The ratio of reaction between the cup and one sphere and that between the two spheres is \includegraphics[width=0.5\linewidth]32.png

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

In symmetric contact problems, geometry decides force ratios.

Answer 1

The Correct Option is C

Step 1: The centres of the spheres form an equilateral triangle with the centre of the cup.
Step 2: Angle between reaction forces is 60^∘.
Step 3: Resolving forces for equilibrium gives fracRcupRₛphₑᵣₑ = 3