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Questions  

Three identical rods each of length L and mass m are joined to form a U-shape as shown in figure .The distance of center of mass of the combined system from the corner  'O' is

a
L2
b
L3
c
8L6
d
13L6

detailed solution

Correct option is D

m1=m, m2=m, m3=m

xcm=m1x1+m2x2+m3x3m1+m2+m3

=0×m×L2×m×Lm+m+m

=m3L23m=3L6=L2

ycm=m1y1+m2y2+my3m1+m2+m3

=m×L2+m×0+m×L23m

=mL2+mL23m=2mL23m=L3

rcm=xcmi+ycmj

=L2i+L3j

=L22+L32

=L24+L29=9L2+4L236

=13L236=13L6

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