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three particle of mass 1 kg,2kg and 3kg are placed at the cornners A, B and C respictavely of an equilateral tringle ABC of edgs 1 m . find the distance of their center of mass from A.
Hi jitendra,
let ABC be the reqd. triangle.
Let A lie at the origin. Therefore, B will automatically lie at (1,0).
mid point of AB hall lie at (0.5,0). Angle A= 60 deg. (equilateral traingle)
Sin 60= CD/AD
√3/2= CD/1
CD=√3/2
Therefore coordinates of C become (0.5, √3/2)
now, COM can be easily calculated.
X= 1(0)+2(1) + 3(0.5)/1+2+3 = 0.583
Y= 1(0) + 2(0)+ 3(√3/2)/6 = √3/4=0.433
distance of com from A= Distance of com from origin = (0.583 i + 0.433 j)
if you wan tto further simplify,
it can easily be calculated as √(0.583)2+(0.433)2
= √0.339+0.187
= 0.725 metres from A
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