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

Question

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

Infinity Learn · Accepted Answer

Choosing the x and y axes as shown in the figure. The coordinates of the vertices of the $$L-shaped$$ lamina is as shown in the figure. Divide the $$L-shaped$$ lamina into three squares each of side $$1$$ m and mass $$1$$ kg $$($$∵ the lamina is $$uniform)$$. By symmetry the centres of mass $$C1$$, $$C2$$ and $$C3$$ of the squares are their geometric centres and have coordinates $$C1(12$$, $$12)$$, $$C2$$ (32$$, $$12) and $$C3(12$$, $$32)$$ respectively.The coordinates of the centre of mass of the $$L-shaped$$ lamina is XCM $$=$$ $$m1x1+m2x2+m3x3m1+m2+m3$$        $$=$$ $$1$$×$$12+1$$×$$32+1$$×$$121+1+1$$ $$=$$ $$56mYCM$$ $$=$$ $$m1y1+m2y2+m3y3m1+m2+m3$$        $$=$$ $$1$$×$$12+1$$×$$12+1$$×$$321+1+1$$ $$=$$ $$56m$$

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

Unlock the full solution & master the concept.

Ready to Test Your Skills?

free study material