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Question

Two equilateral triangular plates are joined together to form the following figure. Density of plate A is 3 times that of plate B. If COM lies inside the plate A at a distance h=3 m from their common side, find out the length of side of each triangular plate.


A
63 m
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B
12 m
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C
63
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D
33 m
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Solution

The correct option is B 12 m
Density of plate A is three times of plate B (Given).


Therefore, if mass of plate B=m
Mass of plate A=3m

Position of COM of triangular plate will be H3 from the base, where H is the height of triangular plate.
Now consider the common side of the plates to be situated on X axis.
Then, y coordinate at which COM of A lies is h1=H3
y coordinate at which COM of B lies is h2=H3

y coordinate of COM of system h=m1h1+m2h2m1+m2
=3m×H3+m(H3)m+3m
=2H12=H6
H=6h=63 (given h=3)
and we know, height of equilateral triangle =32× side of triangle
Then, 63=32× side of triangle
Side of triangle is 12 m.

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