Question 222: Centre of Mass and Rotational Motion

Question

Consider two uniform discs of the same thickness and different radii R1
 = R and R2
 = $$\alpha $$R made of
the same material. If the ratio of their moments of inertia I1
 and I2
, respectively, about their axes
is I1
 : I2
 = 1 : 16 then the value of $$\alpha $$ is :

Accepted Answer

Moment of inertia of disc, $$I = {{M{R^2}} \over 2} = {{\left[ {p\left( {\pi {R^2}} \right)t} \right]{R^2}} \over 2}$$
$$I = K{R^4}$$
$${{{I_1}} \over {{I_2}}} = {\left( {{{{R_1}} \over {{R_2}}}} \right)^4}$$
$${1 \over {16}} = {\left( {{R \over {\alpha R}}} \right)^4} \Rightarrow \alpha  = {\left( {16} \right)^{{1 \over 4}}} = 2$$

Answer

$$\sqrt 2 $$

Answer

2

Answer

$$2\sqrt 2 $$

Answer

4

Centre of Mass and Rotational Motion

Consider two uniform discs of the same thickness and different radii R1 = R and R2 = $\alpha R made of the same material. If the ratio of their moments of inertia I1 and I2 , respectively, about their axes is I1 : I2 = 1 : 16 then the value of \alpha $ is :

Choose the correct answer: