A uniform rectangular thin sheet ABCD of mass M has length a and … - Vidyadip

MCQ

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

A
$\left( {\frac{{5a}}{3},\frac{{5b}}{3}} \right)$
B
$\left( {\frac{{2a}}{3},\frac{{2b}}{3}} \right)$
C
$\left( {\frac{{3a}}{4},\frac{{3b}}{4}} \right)$
✓
$\left( {\frac{{5a}}{12},\frac{{5b}}{12}} \right)$

✓

Answer

Correct option: D.

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

d
$x = \frac{{M\frac{a}{2} - \frac{M}{4} \times \frac{{3a}}{4}}}{{M - \frac{M}{4}}}$

$ = \frac{{\frac{a}{2} - \frac{{3a}}{{16}} \times \frac{{3a}}{4}}}{{\frac{3}{4}}} = \frac{{\frac{{5a}}{{16}}}}{{\frac{3}{4}}} = \frac{{5a}}{{12}}$

$y = \frac{{M\frac{b}{2} - \frac{M}{4} \times \frac{{3b}}{4}}}{{M - \frac{M}{4}}} = \frac{{5b}}{{12}}$

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