There are four rods A,B,C and D of same length l but different mass density d, 2d, 3d, 4d respectively. These are joined to form a square with sides C and D along x and y axis of coordinate axes respectively. Find the coordinate of centre of mass of structure.

 

Dear Student,

Please find below the solution to the asked query:

The coordinates of the centre of mass for each of the rod respectively are A (l/2, l); B (l, l/2); C(l/2, 0) & D(0, l/2).

The masses of the four rods are m, 2m, 3m & 4m‚Äč respectively.

Then the common centre of masses are,

Xcm=ml2+2ml+3ml2+4m0m+2m+3m+4m=4ml10m=2l5Ycm=ml+2ml2+3m0+4ml2m+2m+3m+4m=4ml10m=2l5Therefore, the common centre of mass coordinates are,Xcm,Ycm=2l5,2l5

 


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