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Question

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
L3
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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 A L3
Let us consider the xy 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=33L9=L3
Required distance is L3

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