Question 175: Centre of Mass and Rotational Motion

Question

A uniform rectangular thin sheet ABCD of
mass M has length a and breadth b, as shown
in the figure. If the shaded portion HBGO is
cut-off, the coordinates of the centre of mass
of the remaining portion will be :-
![](https://imagex.cdn.examgoal.net/18hoxe66ijwbyn1xz/7a48fdc2-eb28-4996-ab35-d11fa6bf9f0f/0d72ba70-8391-11e9-8081-1d558b7f1d26/file-18hoxe66ijwbyn1y0.png)

Accepted Answer

X- coordinate of CM of remaining sheet
${X_{cm}} = {{MX - mx} \over {M - m}}$
= ${{\left( {4m} ight) 	imes \left( {{a \over 2}} ight) - M\left( {{{3a} \over 4}} ight)} \over {4m - m}} = {{5a} \over {12}}$
Similarly y
cm
= ${{5b} \over {12}}$
$ 	herefore $ $CM\left( {{{5a} \over {12}},{{5b} \over {12}}} ight)$

Answer

$\left( {{{5a} \over 3},{{5b} \over 3}} \right)$

Answer

$\left( {{{2a} \over 3},{{2b} \over 3}} \right)$

Answer

$\left( {{{5a} \over 12},{{5b} \over 12}} \right)$

Answer

$\left( {{{3a} \over 4},{{3b} \over 4}} \right)$

Centre of Mass and Rotational Motion

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :-

Choose the correct answer: