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

Answer 1

The Correct Option is 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}}{\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} $