Question

As shown in the figure, from a uniform rectangular sheet, a triangular sheet is removed from one edge. The shift of the centre of mass (with respect to $\text{O}$) is

• 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 $6.67\text{cm}$

Let $A_1$ be the area of rectangle and $A_2$ be the mass of triangle removed.
By the symmetry. $Y_{com}$ will be zero.
$A_2=(\frac{1}{2}\times 30\times 20)=300$
$A_1=20\times 60=1200$

Taking origin at $\text{O}$,
Position of centre of mass of rectangle $r_1=0$
Position of center of mass of triangle $\left(r_2\right)=\frac{2}{3}\times$height $=\frac{2}{3}\times 30=20\text{cm}$

Now.
$X_{com}=\frac{A_1{r}_1-A_2{r}_2}{A_1-A_2}$
$=\frac{1200\times 0-300\times 20}{1200-300}$
$=-6.67\text{cm}$

Hence, required shift in center of mass is $6.67\text{cm}$.