Question

Calculate the coordinate of center of a mass of a triangular lamina , whose vertices are (0,0) , (4,0) , (0,4).

Answer 1

centre of mass of triangular lamina is (4/3, 4/3)

let at each vertex placed a point object of mass m.

centre of mass, X_cm = {(m_1x_1+m_2x_2+m_3x_3)/(m_1+m_2+m_3) , (m_1y_1+m_2y_2+m_3y_3)/(m_1+m_2+m_3)}

= {(m × 0 + m × 4 + m × 0)/(m + m + m), (m × 0 + m × m + 0 × 4)/(m + m + m)}

= {4/3, 4/3}

hence, centre of mass of a triangular lamina whose vertices are (0,0) , (4,0) and (0,4) is (4/3, 4/3).

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Answer 2

$\huge\bold\purple{Answer:-}$

let at each vertex placed a point object of mass m.

centre of mass, X_cm = {(m_1x_1+m_2x_2+m_3x_3)/(m_1+m_2+m_3) , (m_1y_1+m_2y_2+m_3y_3)/(m_1+m_2+m_3)}

= {(m × 0 + m × 4 + m × 0)/(m + m + m), (m × 0 + m × m + 0 × 4)/(m + m + m)}

= {4/3, 4/3}

hence, centre of mass of a triangular lamina whose vertices are (0,0) , (4,0) and (0,4) is (4/3, 4/3).