Question

Find the centre of mass of a uniform $L$-shaped lamina (a thin flat plate) with dimensions as shown in the figure alongside. The mass of the lamina is $3kg$.

• A. $(5/6)m,(5/6)m$
• B. $(3/4)m,(3/4)m$
• C. $(5/8)m,(5/8)m$
• D. $(3/5)m,(3/5)m$

Answer 1

Answer: (A)

We can think of the $L$-shape to consist of $3$ squares each of length $1m$ as shown in figure.
The mass of each square is $1kg$ as the lamina is uniform. The centres of masses $C_1,C_2$ and $C_3$ of the squares are (by symmetry) their geometric centres and have coordinates $(1/2,1/2),(3/2,1/2)$ and $(1/2,3/2)$, respectively.
We take the masses of the squares to be concentrated at these points. The centre of mass of the whole $L$-shape $(X,Y)$ is the centre of mass of these mass points.

Hence, $X=\frac{[1(1/2)+1(3/2)+1(1/2)]kg-m}{(1+1+1)kg}$
$=\frac{5}{6}m$
$Y=\frac{[1(1/2)+1(1/2)+1(3/2)]kg-m}{(1+1+1)kg}$
$=\frac{5}{6}m$