Three particles A, B & C of masses 4m,2m & 3m are placed on the vertices of a equilateral triangle of length 2L as shown in the figure.
Find out the perpendicular distance of centre of mass from the side AB.
A
L√3
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B
√3L
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C
√3L2
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D
√3L4
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Solution
The correct option is AL√3 Let us consider the x−y plane and vertex of equilateral triangle at origin and side AB along x axis. The coordinates of the vertices of the triangle will be as shown in figure.
From the figure, we can conclude that the perpendicular distance of COM from side AB is y co-ordinate of COM. therefore, ycom=yAmA+yBmB+yCmC4m+2m+3m =0+0+√3L×3m9m=3√3L9=L√3 ⟹Required distance is L√3