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# a uniform steel rod of 1m length is bent in a 90 deg. angle at its mid point.Determine the position of its centre of mass from the corner at bent.

509 Points
10 years ago

consider that rod is bent such that half part is on +x axis & other half is on +y axis ...

mass of each half is m/2 & length is l/2

center of mass of each section will be at mid point of that section so

center of mass of rod in x axis will be at (l/4,0)

center of mass of rod at y axis will be at (0,l/4)

now , xcom =[ m1x1 + m2x2]/[m1+m2] =[ (m/2)(l/4) + 0]/[m/2 + m/2]

= l/8

ycom = [m1y1 + m2y2]/[m1+m2] = [(m/2)l/4 + 0]/[m/2+m/2] = l/8

rcom = xcom (i) + ycom (j)

=l/8 i + l/8 j

magnitude = l/4root2                     (  from the corner)