TG EAMCET 4 May 2025 Shift 1 Paper

Density ρ, the length of the wire is
L=‌

m

ρ

Since, the wire is bent into a circular ring, its length is equal to the circumference
L=2πR
Therefore, R=‌

L

(2π)

=‌

( m ρ )

(2π)

=‌

m

(2πρ)

The moment of inertia of a circular ring about its diameter is given by
ID=‌

1

2

mR2
Using the parallel axis theorem, the moment of inertia about an axis parallel to the diameter at a distance R (the radius) from the centre is
IT‌=ID+mR2
‌=‌

1

2

mR2+mR2=‌

3

2

mR2
‌=‌

3

2

m(‌

m

2πρ

)2=‌

3m3

8π2ρ2