Question 254: Centre of Mass and Rotational Motion

Question

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $${{7M} \over 8}$$
and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere.
Let I
1
be the moment of inertia of the disc about its axis and I
2
be the moment of inertia of the new sphere
about its axis. The ratio I
1
/I
2
is given by :

Accepted Answer

$${I_1} = {{\left( {{{7M} \over 8}} ight){{\left( {2R} ight)}^2}} \over 2} = {{7M 	imes 4{R^2}} \over {2 	imes 8}} = {{7M{R^2}} \over 4}$$
$${I_2} = {2 \over 5}{M \over 8}{\left( {{R \over 2}} ight)^2} = {{2M} \over {5 	imes 8}}{{{R^2}} \over 4} = {{M{R^2}} \over {80}}$$
$${{{I_1}} \over {{I_2}}} = {{7M{R^2} 	imes 80} \over {4M{R^2}}} = 140$$

Answer

65

Answer

140

Answer

185

Answer

285

Centre of Mass and Rotational Motion

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