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A uniform piece of metal sheet is cut in...

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

Text Solution

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Let the mass per unit area be `sigma`. We divide the structures 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` is `100 sigma`. The coordinates of centre of mass of part `1` are `(5,15)`, that of part `(20,5)` , and that of part `-3` are `(15,25)`.
`X_(cm)=((300 sigma)5+(200 sigma)20+(100 sigma)15)/(600 sigma)~~11.7`
`Y_(cm)=((300 sigma)15+(200 sigma)5+(100 sigma)12)/(600 sigma) ~~13.3`
In vector notation `bar(r)_(cm)=11.7 hati+13.3 hatj`
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