The x, y coordinates of the centre of mass of | vedclass

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(A) Choose the $x$ and $y$ axes as shown in the figure. The $L$-shaped lamina can be divided into three squares,each of side $1\,m$ and mass $1\,kg$ (

Vedclass · Accepted Answer

$\left( \frac{5}{6}\,m, \frac{5}{6}\,m \right)$

Vedclass · Answer

(A) Choose the $x$ and $y$ axes as shown in the figure. The $L$-shaped lamina can be divided into three squares,each of side $1\,m$ and mass $1\,kg$ (since the lamina is uniform).By symmetry,the centres of mass $C_1, C_2,$ and $C_3$ of the squares are their geometric centres. Their coordinates are:$C_1 = \left( \frac{1}{2}, \frac{1}{2} ight), C_2 = \left( \frac{3}{2}, \frac{1}{2} ight), C_3 = \left( \frac{1}{2}, \frac{3}{2} ight)$.The coordinates of the centre of mass of the $L$-shaped lamina are given by:$X_{CM} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3}{m_1 + m_2 + m_3} = \frac{1 	imes \frac{1}{2} + 1 	imes \frac{3}{2} + 1 	imes \frac{1}{2}}{1 + 1 + 1} = \frac{5/2}{3} = \frac{5}{6}\,m$.$Y_{CM} = \frac{m_1 y_1 + m_2 y_2 + m_3 y_3}{m_1 + m_2 + m_3} = \frac{1 	imes \frac{1}{2} + 1 	imes \frac{1}{2} + 1 	imes \frac{3}{2}}{1 + 1 + 1} = \frac{5/2}{3} = \frac{5}{6}\,m$.Thus,the centre of mass is at $\left( \frac{5}{6}\,m, \frac{5}{6}\,m ight)$.

The $x, y$ coordinates of the centre of mass of a uniform $L$-shaped lamina of mass $3\, kg$ are

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