Question

Find coordinates of the centre of mass of a uniform $L-$shaped lamina (a thin flat plate) wrt origin, having dimensions as shown in figure. (Consider mass of lamina as $3mkg$)

• A. $(\frac{5}{6};\frac{5}{6})$
• B. $(\frac{5}{6},\frac{7}{6})$
• C. $(\frac{5}{3},\frac{5}{6})$
• D. $(\frac{5}{6},\frac{5}{7})$

Answer 1

The correct option is A $(\frac{5}{6};\frac{5}{6})$

From figure L shaped lamina can be considered as combination of
(i)A square of mass $m$ having centre at $(\frac{1}{2},\frac{3}{2})$
(ii)A rectangle of mass $2m$ having centre at$(1,\frac{1}{2})$
($\because$ Area of rectangle is double that of area of square. So, mass of the rectangle is also double to that of mass of square)

Finding position of COM,
$x_{cm}=\frac{2m\times 1+m\times \frac{1}{2}}{3m}=\frac{5}{6}$
$y_{cm}=\frac{2m\times \frac{1}{2}+m\times \frac{3}{2}}{3m}=\frac{5}{6}$


So, Coordinates of COM are $(\frac{5}{6},\frac{5}{6})$