Question 215: Centre of Mass and Rotational Motion

Question

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes
perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is :
![](https://imagex.cdn.examgoal.net/jgy2xukfavsssy/867e4c46-7e0a-42b0-bed4-407149725c32/4567bb20-fb21-11ea-8293-3b6cc591631c/file-jgy2xukfavsssz-276w.png)

Accepted Answer

${I_O} = {M \over {12}}\left( {{a^2} + {b^2}} ight)$ = ${M \over {12}}\left[ {{{80}^2} + {{60}^2}} ight]$
I
O'
= I
O
+ Md
2
{parallel axis theorem}
= ${M \over {12}}\left[ {{{80}^2} + {{60}^2}} ight]$ + M[50]
2
$ 	herefore $ ${{{I_O}} \over {{I_{O'}}}}$ = ${{{M \over {12}}\left[ {{{80}^2} + {{60}^2}} ight]} \over {{M \over {12}}\left[ {{{80}^2} + {{60}^2}} ight] + M{{\left[ {50} ight]}^2}}}$ = ${1 \over 4}$

Answer

${1 \over 2}$

Answer

${1 \over 4}$

Answer

${1 \over 8}$

Answer

${2 \over 3}$

Centre of Mass and Rotational Motion

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is :

Choose the correct answer: