Question

Four bodies of masses 8 kg, 2 kg, 4 kg and 2 kg are placed at the four corners A, B, C and D respectively of a square ABCD of diagonal 80 cm. The distance of the center of mass of the system from the corner A is:

• A. 30 cm
• B. 40 cm
• C. 60 cm
• D. 20 cm

Hint:

The center of mass of a system can be found by taking the weighted average of the positions of all masses involved.

Answer 1

The Correct Option is A

- Given a square with a diagonal of 80 cm, each side length is \( 40\sqrt{2} \) cm. Calculate the coordinates as \( A(0, 0) \), \( B(40\sqrt{2}, 0) \), \( C(40\sqrt{2}, 40\sqrt{2}) \), \( D(0, 40\sqrt{2}) \).
- Using the formula for the center of mass: \[ x_{\text{cm}} = \frac{m_A \times 0 + m_B \times 40\sqrt{2} + m_C \times 40\sqrt{2} + m_D \times 0}{m_A + m_B + m_C + m_D} = 15\sqrt{2} \, \text{cm} \] \[ y_{\text{cm}} = \frac{m_A \times 0 + m_B \times 0 + m_C \times 40\sqrt{2} + m_D \times 40\sqrt{2}}{m_A + m_B + m_C + m_D} = 15\sqrt{2} \, \text{cm} \]
- The distance from corner A is then: \[ \sqrt{(15\sqrt{2})^2 + (15\sqrt{2})^2} = 30 \, \text{cm} \]