Question

Three identical spheres, each of mass 'm' kg, are kept as shown in the figure, touching each other, with their centers on a straight line. If their centers are marked as A, B, C respectively, the distance of center of mass of the system from A is

• A. \(\frac{AB+BC}{3}\)
• B. \(\frac{AB+AC}{3}\)
• C. \(\frac{AC+BC}{2}\)
• D. \(\frac{AB+BC+AC}{3}\)

Hint:

Take A at the origin; the centre of mass is the average of the positions of the centres.

Answer 1

The Correct Option is B

Step 1: Use equal masses
With equal masses, the centre of mass is the plain average of the three centre positions.

Step 2: Measure from A
Positions from A are $0$, $AB$ and $AC$, so the average is $\dfrac{AB+AC}{3}$, option (B).

Final Answer:
The distance from A is $(AB+AC)/3$, option (B). \[ \boxed{\dfrac{AB+AC}{3}} \]