Question

A uniform square sheet has a side length of 2r if one of the quadrant is removed the shift in the centre of masses is

Answer 1

Explanation:

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= 2R

Let x1 and x2 be the x components of centre of masses of m1 and m2 respectively.

Let y1 and y2 be the y components of centre of masses of m1 and m2 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

2

2

R

2

m

2

=m(4R

2

−π

2

2

R

2

)

Centre of mass of m

1

and m

2

is at origin.

0=π

2

2

R

2

2

R

+(4R

2

−π

2

2

R

2

)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

Answer 2

Answer:

root 3 is answer

Explanation:

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