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A uniform rod of mass m and length l is bend to form A right angled triangle as shown in figure locate the centre of mass of rod

A uniform rod of mass m and length l is bend to form A right angled triangle as shown in figure locate the centre of mass of rod

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Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
As the rod is uniform and the three sides of triangle contributes the total length.
that is to say that ------->
let suppose the sides be x and y respectively.
x + y + root(x^2 + y^2) = l …..........(1)
and from geometry,
1/root3 = x/y
y = root3 * x...............(2)
solve both eqns first and write x and y first in terms of l.
then suppose taking origin at B point we will write their x and y axis com.
thus,
com for AB rod = > (0,x/2)
com for BC rod = > (y/2,0)
com for rod AC = > (find its coordinates at half of root(x^2 + y^2)
Then apply the formulae:
Xcom =(m*x1 + m*x2)/(total mass)
 

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