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Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is:

1. 40 cm
2. 45 cm
3. 50 cm
4. 30 cm

Correct answer: 45 cm

Solution

The center of mass is calculated using the formula: \( x_{cm} = \frac{\sum m_i x_i}{\sum m_i} \). Substituting the values: \( x_{cm} = \frac{(300 \times 0) + (500 \times 40) + (400 \times 70)}{300 + 500 + 400} = \frac{0 + 20000 + 28000}{1200} = 45 \, \text{cm} \).

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