Question

From the circular disc of radius 4r two small discs of radius r are cut off . the centre of mass of the new structure will be

Answer 1

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Answer 2

Given:

Circular discs = 2

Radius = 4r

To Find:

Centre of mass of the new structure will

Solution:

Centre of mass of circular disc of radius 4r = (0,0)  

Centre of mass of the upper disc = (0, 3r)  

Centre of mass of the lower disc = (3r, 0)  

Let the mass of complete disc be = M

Thus, mass of the cut out disc = M/16

Therefore, centre of mass of the new structure is given by -

x = m1x1 - m2x2 - m3x3/ m1 - m2 - m3

= m (0) -  - m/16 (0) - m/16 ( 3r)/ m - m/16 - m/16

= -3r/14

Similarly for y, the vector position will be -  

= - 3r/14 ( i +j)

Answer: Centre of mass of the new structure is  - 3r/14 ( i +j)