An equilateral traingular plate of mass `4m` of side a is kept as shown. Consider two cases: (i) a point mass `4m` is placed at the vertex P of the plate (ii) a point mass `m` is placed at the vertex R of the plate. In both cases the x-coordinate of centre of mass remains the same. Then x coordinate of centre of mass of the plate is A. (a) `a/3`B. (b) `a/6`C. (c) `(6a)/(7)`D. (d) `(2a)/(3)`

An equilateral traingular plate of mass `4m` of side a is kept as show

1.	An equilateral traingular plate of mass `4m` of side a is kept as shown. Consider two cases: (i) a point mass `4m` is placed at the vertex P of the plate (ii) a point mass `m` is placed at the vertex R of the plate. In both cases the x-coordinate of centre of mass remains the same. Then x coordinate of centre of mass of the plate is A. (a) `a/3`B. (b) `a/6`C. (c) `(6a)/(7)`D. (d) `(2a)/(3)`
Answer» Correct Answer - B `((4m)X_1+(4m)(a/2))/(8m)=((4m)X_1+(m)(a))/(5m)` Solving this equaiton, we get `X_1=X`-coordinate of COM of plate `=a/6`

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