Question

A uniformly thick plate in the shape of an arrowhead has dimensions as shown. The center of mass of the system lies at a point:

• A. $1.5cm$ to the right of $O$
• B. $3cm$ to the right of $O$
• C. $O$ itself
• D. $1cm$ to the right of $O$

Answer 1

Answer: (D)

$1cm$ to the right of $O$

COM of an isosceles triangle is on median and $h/3$ above the base.
So, COM of bigger triangle is $3$ cm from base and that of lower (hollow ) triangle is $1cm$. Calculating COM of the system. (hollow triangle is considered as negative mass )

$COM=\frac{m_1{r}_1+m_2{r}_2}{m_1+m_2}=\frac{(\rho \times 0.5\times 9\times 6)\times 3-(\rho \times 0.5\times 3\times 6)\times 1}{\rho \times 0.5\times 9\times 6-\rho \times 0.5\times 3\times 6}\text{(as thickness is same for smaller and bigger}$

$\text{triangle so it is cancelled in numerator and in denominator})$

$=\frac{72}{18}=4cm$

From the base i.e. , $1cm$ to right of $O$.