Question
A metal sheet $$14\,cm \times 2\,cm$$ of uniform thickness is cut into two pieces of width $$2\,cm.$$ The two pieces are joined and laid along $$XY$$ plane as shown. The centre of mass has the coordinates
A metal sheet $$14\,cm \times 2\,cm$$ of uniform thickness is cut into two pieces of width $$2\,cm.$$ The two pieces are joined and laid along $$XY$$ plane as shown. The centre of mass has the coordinates
A.
$$\left( {1,1} \right)$$
B.
$$\left( {\frac{7}{2},\frac{7}{2}} \right)$$
C.
$$\left( {\frac{{13}}{4},\frac{9}{4}} \right)$$
D.
$$\left( {\frac{{12}}{7},\frac{8}{7}} \right)$$
Answer :
$$\left( {\frac{{13}}{4},\frac{9}{4}} \right)$$
Solution :
$$\eqalign{ & {X_{cm}} = \frac{{m \times 5.5 + 1 \times m}}{{2m}} = \frac{{6.5}}{2} = \frac{{13}}{4}cm. \cr & {Y_{cm}} = \frac{{m \times 3.5 + 1 \times m}}{{2m}} = \frac{{4.5}}{2} = \frac{9}{4}cm. \cr} $$
$$\eqalign{ & {X_{cm}} = \frac{{m \times 5.5 + 1 \times m}}{{2m}} = \frac{{6.5}}{2} = \frac{{13}}{4}cm. \cr & {Y_{cm}} = \frac{{m \times 3.5 + 1 \times m}}{{2m}} = \frac{{4.5}}{2} = \frac{9}{4}cm. \cr} $$
