IIT JEE , AIEEE Forum - Physics , Mechanics

gayathri

Hi,
     I have doubt in these 2 problems.it sounds simple. help me to do it.

1.masses m, 2m, 3m occupy the vertices of an equilateral triangle of side a.
   locate the centre of mass of the system.
2.masses m, 2m, 3m, 4m occupy the vertices of a squre of side a.loacate centre    of mass of the system.

please help.

gayathri

edison

Consider an equilateral

ABC with one of the vertex say A on the origin and side AB along X-axis. So coordinates of the vertices can be assigned as

A(0,0); B(a,0) and C(a/2, a

3/2)

If masses m, 2m and 3m are placed on the vertices A, B and C respectively then coordinates of center of mass C(X,Y) can be expressed as

X = [0*m + a*2m + (a/2)*3m]/6m

or X= 7a/12

Similarly Y = [0*m + 0*2m + (a

3/2)*3m]/6m = a

3/4

so Y = a3/4

Now consider coordinates of square ABCD with side 'a' to be

A(0,0); B(0,a); C(a,a) and D(0,a) with masses m, 2m, 3m and 4m respectively and try to locate the center of mass.

vaibhav.best

A 1. If we take the x-axis along m & 3m then the coordinates of COM is

( 2a/3 , a/3 ) .........

A 2. If we take x-axis along m & 2m & y-axis along 4m respectively then the

coordinates of COM is ( a/2 , 7a/10 ) .................

uday_zingtudor

1) x= m(0)+2m(1/2)+3m(1)/m+2m+3m

=4m/6m = 2/3

y= m(0)+2m(^{[ ]}

3/2)+3m(0)/6m

=m(root3)/6m = 1/2root3

(x,y)=(2/3,1/2

3)

do the second one in the similar way

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