Question

three particles each of mass 5 kg at the corner of equilateral triangle of Side 2 into root 3 is one of the particle is removed the shift in the centre of mass is

Answer 1

Final Answer : 1/2 m

Steps and Understanding:

1) Let A be origin and By using properties of equilateral triangle, we get other points B, C

as

A= (0,0)

B = (√3/2, 3/2)

C= (√3,0)

2) Here, all 3 masses are same, so

Centre of mass position will be same as Centrifugal of triangle ABC,

So,

D = (( 0 + √3/2 + √3)/3 , (0+3/2+0)/3 )

= (√3/2 , 1/2)

So, Initial position of Centre of Mass is

R(i) = (√3/2,1/2)

3) Now, we have to remove any mass :

To make calculations easy, let us remove

Mass at point B.

Now,

Required masses : A, C.

Since, masses are same so,

Position of Centre of Mass will be same as Mid point of A and C.

So,

R(f) = (√3/2,0)

5) Now,

R(f) - R(i) = (0, -1/2)

Magnitude = 1/2 m

So, shift in Centre of Mass = 1/2m .