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Find the centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is 3 kg. |
Answer» Solution :Choosing the X and Y axes as shown in Fig. 7.11 we have the coordinates of the vertices of the L-shaped lamina as given in the figure. We can think of the L-shape to consist of 3 squares each of length 1M. The mass of each SQUARE is 1kg, since the lamina is uniform. The centres of mass `C_(1), C_(2) and C_(3)` of the squares are, by symmetry, their geometric centres and have coordinates (1/2,1/2), (3/2,1/2), (1/2,3/2) respectively. We take the masses of the squares to be concentrated at these points. The centre of mass of the whole L shape (X, Y) is the centre of mass of these mass points.  Hence `X=([1(1//2)+1(3//2)+1(1//2)]kgm)/((1+1+1)kg)=(5)/(6)m` `Y=([1(1//2)+1(1//2)+1(3//2)]kgm)/((1+1+1)kg)=(5)/(6)m` The centre of mass of the L-shape lies on the line OD. We could have guessed this without calculations. Can you TELL why? SUPPOSE, the three squares that make up the L shaped lamina of Fig. 7.11 had different masses. How will you then determine the centre of mass of the lamina? |
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