Three identical spheres, each of radius 3 cm, are placed on a horizontal surface touching one another. The distance of the centre of mass of the system from any centre of a sphere is ______ cm.
Physics · Mixed Chapter
JEE Main Practice

Question

Three identical spheres, each of radius 3 cm, are placed on a horizontal surface touching one another. The distance of the centre of mass of the system from any centre of a sphere is ______ cm.

G1 Physics · Accepted Answer

Step 1: Centres of three touching spheres form an equilateral triangle of side a = 2r = 6 cm. Step 2: Equal sphere masses put the centre of mass at the triangle centroid. Step 3: Distance from any vertex to centroid = (2/3) × altitude = (2/3) × (√3/2)a = a/√3. Step 4: Distance = 6/√3 = 2√3 = 3.46410 cm. Final answer: 3.464 cm.