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
Answers
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
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