the centre of mass of a uniform rod of length 4l is located at
Answers
Consider the thin rod be divided into 4 parts 2 on the left side and 2 on the right side. Mass of each part =4M/4= M
Length of each portion =4l/4=l
Considering the extreme left portion
M I about an axis through CG perpendicular to the plane of paper =Ml^2/12
Distance of CG from axis through O=
= √{l² +(l)² /4}
Hence MI about the axis through O
=Ml²/12+M[ √{l²+(l/2)²}] ²=Ml²/12+5Ml²/4=4Ml²/3
MI of second left portion about O=Ml²/3
Hence MI of left part about O =4Ml²/3+Ml²/3
=5Ml²/3
MI of the whole rod About an axis through O
Perpendicular to the plane of paper =2*(5Ml²/3)
=10Ml²/3
Hence (b)
Explanation:
The center of mass of a uniform rod is at the center of the rod. So, the center of mass of a uniform rod that extends along the x axis from x=0 to x=4L is at (2L, 0).
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