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Question: Three identical spheres of mass $M$ each are placed at the corners of an equilateral triangle of sid...

Three identical spheres of mass MM each are placed at the corners of an equilateral triangle of side 2 m. Taking one of the corners as the origin as shown in the figure, the position vector of the centre of mass is

Answer

i^+33j^\hat{i} + \frac{\sqrt{3}}{3} \hat{j}

Explanation

Solution

  1. Identify the coordinates of the three masses based on the given figure and information.

  2. Use the formula for the position vector of the center of mass of a system of particles: R⃗CM=∑mir⃗i∑mi\vec{R}_{CM} = \frac{\sum m_i \vec{r}_i}{\sum m_i}.

  3. Since the masses are identical, the formula simplifies to R⃗CM=∑r⃗iN\vec{R}_{CM} = \frac{\sum \vec{r}_i}{N}, where N is the number of particles.

  4. Substitute the position vectors of the three masses into the simplified formula and perform the vector addition and division by 3.

  5. The resulting vector is the position vector of the center of mass.