Question

As shown in the figure, a triangular sheet is removed from a uniform rectangular sheet. Then, shift of the centre of mass for the new shape will be:

• A. $3.2\text{cm}$
• B. $4.2\text{cm}$
• C. $5.67\text{cm}$
• D. $6.67\text{cm}$

Answer 1

The correct option is D $6.67\text{cm}$

$\text{COM}$ of original rectangular sheet will be at $\text{O}(0,0)$
Area of rectangular sheet $A_1=20\times 60=1200{\text{cm}}^2$
Area of triangular part
$A_2=\frac{1}{2}\times 20\times 30=300{\text{cm}}^2$

Let the x-coordinates of $\text{COM}$ of rectangular shape and triangular shape be $x_1$ and $x_2$ resepctively.
Then, $x_1=0$

$\because$Position of $\text{COM}$ for triangle from it's vertex ($\text{O}$): $=\frac{2}{3}\times h=\frac{2}{3}\times 30=20\text{cm}$
$\therefore x_2=(0+20)=20\text{cm}$

Considering the removed triangular shape as $-ve$ mass superimposed on whole rectangular shape, and applying the formula by considering shapes as point masses at their respective $\text{COM}$, the x-coordinate for $\text{COM}$ of remaining part is:


$x_{\text{CM}}=\frac{A_1{x}_1-A_2{x}_2}{A_1-A_2}$

$\therefore x_{\text{CM}}=\frac{1200\times 0-300\times 20}{1200-300}=-6.67\text{cm}$

Hence, $\text{COM}$ of new shape shifts by $6.67\text{cm}$ along -ve x-axis or leftwards.