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STANDARDPhysics-System of Particles and Rotational Motion

STANDARD Physics Centre of Mass MCQ Question

Type: MCQ-numerical-Hard-Class 11

Three particles of masses 1 kg, 32\frac{3}{2} kg, and 2 kg are located at the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are

Question diagram
A

(5a9,2a33)\left( \frac{5a}{9}, \frac{2a}{3\sqrt{3}} \right)

B

(2a33,5a9)\left( \frac{2a}{3\sqrt{3}}, \frac{5a}{9} \right)

C

(5a9,2a3)\left( \frac{5a}{9}, \frac{2a}{\sqrt{3}} \right)

D

(2a3,5a9)\left( \frac{2a}{\sqrt{3}}, \frac{5a}{9} \right)

Correct Answer

Option A

Detailed Explanation

The center of mass is calculated using the formula ∑mixi∑mi\frac{\sum m_ix_i}{\sum m_i} for x-coordinate and ∑miyi∑mi\frac{\sum m_iy_i}{\sum m_i} for y-coordinate. Substituting the given values, the coordinates are (5a9,2a33)\left( \frac{5a}{9}, \frac{2a}{3\sqrt{3}} \right).

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