A uniform piece of metal sheet is cut in the form as shown in the fig. Locate the center of mass of the piece.

A uniform piece of metal sheet is cut in the form as shown in the fig.

1.	A uniform piece of metal sheet is cut in the form as shown in the fig. Locate the center of mass of the piece.
Answer» Solution : Let the mass per unit area be `SIGMA` We divide the STRUCTURE into parts 1, 2 and 3. The mass of PART 1 is 300 `sigma`, mass of part 2 is 200 `sigma` and that of part 3 in 100 `sigma`. The coordinates of centre of mass of part 1 are (5, 15), that of part 2 are (20,5), and that of part 3 are (15, 25) Using the Eq. `x_(cm)=((300sigma)5+(200sigma)20+(100sigma)15)/(600sigma)~~11.7` `y_(cm)=((300sigma)15+(200sigma)5+(100sigma)25)/(600sigma)~~13.3` In vector notation `barr_(cm)=11.7hati+13.3hatj`