A uniform piece of metal sheet is cut in the form as shown in the fig. Locate the centre 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 centre 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+(200 sigma)20+(100 sigma)15)/(600 sigma)~~11.7` `y_(cm)=((300 sigma)15+(200 sigma)5+(100 sigma)25)/(600 sigma)~~13.3` In vector notation `bar(r_(cm))=11.7hat(i)+13.3 HAT(j)`