AP EAMCET Engineering 21 Sep 2020 Shift 2 Paper

(a) Suppose, the mass of circular disc is M.
A square portion of diagonal r is cut from it.
Assuming centre of mass of circle to be origin.
Centre of mass of square portion will be at distance ‌

r

2

from it.
∴ Side of square =‌

r

√2

Area of square =(‌

r

√2

)2=‌

r2

2

Mass of square, m=M×‌

r2∕2

πr2

m=‌

M

2π

Centre of a mass of remaining disc from the centre of disc,
‌x=M×0−‌

m×r∕2

M−m

=‌

− M 2π × r 2

M−‌ M 2π

=‌

−r

4π−2

⇒‌x=‌

r

2−4π