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 D 12 mDensity 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=6√3 (given h=√3) and we know, height of equilateral triangle =√32× side of triangle Then, 6√3=√32× side of triangle ⇒ Side of triangle is 12 m.

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