Question

A uniform square sheet has a side length of 4R. If one of the quadrants is removed, the shift in the centre of mass plz answer it

Answer 1

Answer:

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Explanation:

ANSWER

Let

m

1

be the mass of circular sheet of radius 

R

and

m

2

be the mass of the remaining portion of square sheet after removing the circular sheet.

Side of square 

=

2R

Radius of circle= 

2

R

Let

x

1

and

x

2

be the x components of centre of masses of 

m

1

and

m

2

respectively.

Let

y

1

and

y

2

be the y components of centre of masses of

m

1

and

m

2

respectively.

x

1

=

2

R

y

1

= 

2

R

x

2

x

y

2

y

Let the centre of square sheet be at origin.

Let 

m

 be the mass per unit area.

m

1

mπ

22

R2

4R

2

−

m

2

mπ

22

R2

Centre of mass ofm

1

andm

2

is at origin.

0=

π

22

R2

2

R

+

(4R

2

−

π

22

R2

)x

x=-π

2(16−π)

R

Similarly 

y=

−π

2(16−π)

R

Centre of mass of

m

2

is at (

π

2(16−π)

R

,

π

2(16−π)

R

)

Distance of it from origin is 

π

2

×(16−π)

R