Question

4 masses are placed at 4 corners of square ABCD. If one mass is removed from the corner B, then the centre of mass lies in the line joining

• A. \( \text{AC} \)
• B. \( \text{AB} \)
• C. \( \text{AD} \)
• D. \( \text{BC} \)

Hint:

When removing a mass from a system, the centre of mass is affected by the masses left and their positions. For symmetry, the center of mass often lies along a line joining the remaining points.

Answer 1

The Correct Option is B

Let the masses placed at the corners of the square ABCD be \( m_1, m_2, m_3, \) and \( m_4 \), with \( m_2 \) removed from corner B. The remaining three masses are at the corners A, C, and D. The centre of mass of the remaining system will lie on the line joining A and C. To find the centre of mass for the system, we can use the formula for the centre of mass of multiple point masses: \[ x_{\text{cm}} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3}{m_1 + m_2 + m_3} \] The \( x \)-coordinates of the points A, C, and D are \( x_A, x_C, x_D \), and similarly for the \( y \)-coordinates. The centre of mass lies on the line joining points A and B.
Thus, after removing the mass at B, the center of mass will lie on the line joining \( A \) and \( B \), and the correct answer is \( \text{AB} \).