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Units And Measurement

Question
CBSEENPH11017433

A thin uniform flat plate of mass 4-5 kg is in the form of L shape lamina as shown in figure.

Find the position of center of mass.


Solution
As shown in the figure below, the lamina consists of three squares, each of side 2 unit. 
Therefore, the coordinates of the centre of mass of three squares are C1 ↔ (1,1), C2 ↔ (3,1) and C3 ↔ (1,3).
Let m be the mass of each square.
Therefore, coordinates of centre of mass of lamina are, 


straight X space equals space fraction numerator straight m subscript 1 straight x subscript 1 plus straight m subscript 2 straight x subscript 2 plus straight m subscript 3 straight x subscript 3 over denominator straight m subscript 1 plus straight m subscript 2 plus straight n 1 subscript 3 end fraction space

space space space equals space fraction numerator straight m cross times 1 plus straight m cross times 3 plus straight m cross times 1 over denominator straight m plus straight m plus straight m end fraction

space space space equals 5 over 3 space unit space

space straight Y space equals space fraction numerator straight m subscript 1 straight y subscript 1 plus straight m subscript 2 straight y subscript 2 plus straight m subscript 3 straight y subscript 3 over denominator straight m subscript 1 plus straight m subscript 2 plus straight n 1 subscript 3 end fraction space

space space space space space equals space fraction numerator straight m cross times 1 plus straight m cross times 1 plus straight m cross times 3 over denominator straight m plus straight m plus straight m end fraction

space space space space equals 5 over 3 space unit space