Question

Two discs have their radii in ratio of 3:1 and masses in ratio of 1:2. Find ratio of their moment of inertia (given that I = 1/2 MR²)​
please help​

Answer 1

Given : -

Ratio of masses = 1:2

Ratio of radii = 3:1

To Find : -

Ratio of moment of inertia of two discs.

Solution : -

Moment of inertia is a rotational analogue of mass.

It is a tensor physical quantity.

SI unit : kg m²

Moment of inertia of a disc about an axis passing through its center and perpendicular to plane is given by

$\bf I = \dfrac{MR^2}{2}$

Taking ratio of moment of inertia of both discs, we get

\longrightarrow \sf \dfrac{I}{I^'}= \dfrac{\dfrac{MR^2}{2}}{\dfrac{M^{'}R^{'2}}{2}}

\longrightarrow\sf \dfrac{I}{I^'} = \dfrac{M}{M^'} \times \dfrac{R^2}{R^{'2}}

\longrightarrow \sf \dfrac{I}{I^'} = \dfrac{1}{2} \times \left( \dfrac{3}{1} \right)^2

\longrightarrow \sf \dfrac{I}{I^'} = \dfrac{9}{2}

$\longrightarrow \underline{\boxed{\bf I:I^{'} = 9:2}}$