Question

Four two-dimensional objects are shown below, with a square grid drawn for reference. Each white square is empty, while each green square contains uniformly dense mass. For each object, choose the row (1-4) and column (a-d) in which the object\'s center of mass is located.

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Answer 1

Taking object in clocwise order the the loacation of center of mass for object.

This can be find out by simply assuming X axis along row while Y axis aling Column

A) let X is x-coordinate center of mass of object 1 then X= M( 2+3+1+2+3+1+2)/7M= 2

let Yis y-coordinate center of mass of object 1 then Y= M( 2+3+1+2+3+1+2)/7M= 2

therefor center of mass is 2b.

B) let X is x-coordinate center of mass of object 2 then X= M( 1+2+3+1+3+1+2+3)/2M= 2

let Yis y-coordinate center of mass of object 2 then Y= M(1+2+3+1+3+1+2+3)/8M= 2

therefor center of mass is 2b

C) let X is x-coordinate center of mass of object 3 then X= M( 3+2+3)/3M= 2.67

let Yis y-coordinate center of mass of object 1 then Y= M( 3+2+3)/3M= 2.67

therefor center of mass is 3c

D) let X is x-coordinate center of mass of object 4 then X= M( 2+3+1+2+3+4+1+3+4+1+2+3)/12M= 2.42

let Yis y-coordinate center of mass of object 1 then Y= M( 2+3+4+1+2+4+1+2+3+4+2+3)/12M= 2

therefor center of mass is 3c