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 :-

• A. $(\frac{2a}{3},\frac{2b}{3})$
• B. $(\frac{5a}{3},\frac{5b}{3})$
• C. $(\frac{3a}{4},\frac{3b}{4})$
• D. $(\frac{5a}{12},\frac{5b}{12})$

Answer 1

The correct option is D $(\frac{5a}{12},\frac{5b}{12})$

$x=\frac{M\frac{a}{2}-\frac{M}{4}\times \frac{3a}{4}}{M-\frac{M}{4}}$
$=\frac{\frac{a}{2}-\frac{3a}{16}}{\frac{3}{4}}=\frac{\frac{5a}{16}}{\frac{3}{4}}=\frac{5a}{12}$
$y=\frac{M\frac{b}{2}-\frac{M}{4}\times \frac{3b}{4}}{M-\frac{M}{4}}=\frac{5b}{12}$