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masses 8,2,4,2 kg are placed at the corners A,B,C,D of a square ABCD whose diagonal is 80cm . the distance of COM from A is 

 

Asked by 1901020030 26th February 2022, 8:54 PM
Answered by Expert
Answer:
Diagonal of square = 80 cm
By pythagoras theorem each side of the sqaure will be = 40√2 = 56.56 = 0.56 m 
m1 = 8 kg, m2 = 2 kg, m3 = 4 kg, m4 = 2 kg 
 r with rightwards arrow on top equals open parentheses x i with hat on top plus y j with hat on top close parentheses equals fraction numerator open parentheses m subscript 1 x subscript 1 space plus space m subscript 2 x subscript 2 space plus space m subscript 3 x subscript 3 space plus m subscript 4 x subscript 4 close parentheses over denominator m subscript 1 plus m subscript 2 plus m subscript 3 plus m subscript 4 end fraction 
Thus, centre of mass is 
=fraction numerator 8 cross times left parenthesis 0 i with hat on top plus 0 j with hat on top right parenthesis plus space 2 left parenthesis 0 i with hat on top plus 0.56 j with hat on top right parenthesis plus 4 left parenthesis 0.56 i with hat on top plus 0.56 j with hat on top right parenthesis plus 2 left parenthesis 0.56 i with hat on top plus 0 j with hat on top right parenthesis over denominator 8 plus 2 plus 4 plus 2 end fraction
equals space fraction numerator 0 plus 1.12 j with hat on top space plus space 2.24 space i with hat on top plus space 2.24 space j with hat on top plus space 1.12 i with hat on top over denominator 16 end fraction
x equals fraction numerator 3.36 space i with hat on top space plus space 3.36 space j with hat on top over denominator 16 end fraction equals 0.21 space i with hat on top plus 0.21 j with hat on top space
D i s tan c e space o f space C O M space f r o m space A space i s space
equals space square root of left parenthesis x minus 0 right parenthesis squared space plus left parenthesis space y minus 0 right parenthesis squared end root space equals space square root of x squared plus y squared end root space
equals space square root of 0.21 squared plus 0.21 squared end root space equals space square root of 0.044 plus 0.044 end root space equals space 0.299 almost equal to 0.30 space m space equals space 30 space c m space
Answered by Expert 28th February 2022, 1:15 PM
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