Two discs of same mass and same thickness ( t ) are made from two… - Vidyadip

MCQ

Two discs of same mass and same thickness ( $t$ ) are made from two different materials of densities ' $d_1$ ' and ' $d_2$ ' respectively. The ratio of the moment of inertia $I_1$ to $I_2$ of two discs about an axis passing through the centre and perpendicular to the plane of disc is

A
$d_1: d_2$
✓
$d_2: d_1$
C
$1: d_1 d_2$
D
$1: d_1^2 d_2$

✓

Answer

Correct option: B.

$d_2: d_1$

(b) : Moment of Inertia of disc $=\frac{1}{2} m R^2$

$\frac{\text { mass }}{\text { density }}=$ volume

Volume of disc $=\pi R^2 t$

So, $\pi R_1^2 t=\frac{m}{d_1} ; \pi R_2^2 t=\frac{m}{d_2}$

$
\frac{R_1}{R_2}=\sqrt{\frac{d_2}{d_1}} ; \frac{I_1}{I_2}=\frac{\frac{1}{2} m R_1^2}{\frac{1}{2} m R_2^2}=\frac{d_2}{d_1}
$

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