Question

the moment of inertia of a disc of mass 2kg and radius 20cm about tangent line parallel ta the axis passing through center​

Answer 1

moment of inertia about tangential line = 0.1 kgm²

we know, moment of inertia of disc about an axis passing through its centre and perpendicular to its plane is given, I = 1/2 MR²

from perpendicular axis theorem,

moment of inertia about its diameter, I' = I/2 = 1/4 MR²

now from parallel axis theorem,

moment of inertia about tangential line parallel to the axis passing through its centre, I" = I' + MR²

= 1/4 MR² + MR²

= 5/4 MR²

= 5/4 × 2 kg × (20cm)²

= 5/2 × 400 × 10^-4 kgm²

= 1000 × 10^-4 kgm²

= 0.1 kgm²

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Answer 2

$\huge\bold\purple{Answer:-}$

we know, moment of inertia of disc about an axis passing through its centre and perpendicular to its plane is given, I = 1/2 MR²

from perpendicular axis theorem,

moment of inertia about its diameter, I' = I/2 = 1/4 MR²

now from parallel axis theorem,

moment of inertia about tangential line parallel to the axis passing through its centre, I" = I' + MR²

= 1/4 MR² + MR²

= 5/4 MR²

= 5/4 × 2 kg × (20cm)²

= 5/2 × 400 × 10^-4 kgm²

= 1000 × 10^-4 kgm²

= 0.1 kgm²