Question 258: 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 I1 be the moment of inertia of the disc about its axis and I2 be the moment of inertia of the new sphere
about its axis. The ratio I1/I2 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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