Question

What do you understand by rigid body & Find the centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown. The mass of lamina is 3 kg.

Answer 1

Rigid body

In physics, a rigid in a solid body in which deformation is zero or so small it can be neglected. The distance between any two gives points on a right body remains constant.

Since this L-shaped lamina is symmetrical and of weight 3 kg each of the squares will be of 1 kg.

for square, the center of mass will be there geometrical center showing in figure

1) $(0.5,1.5)$

2) $(0.5,0.5)$

3) $(1.5,0.5)$

for (1), (2) & (3) squares respectively and there we can find the center a mass

$COM=\frac{m_1\overrightarrow{r_1}+m_2\overrightarrow{r_2}+m_3\overrightarrow{r_3}}{m_1+m_2+m_3}$

$=\frac{1}{3}[0.5\hat{x}+0.5\hat{j}+0.5i+1.5\hat{j}+1.5\hat{i}+0.5\hat{j}]$

$=\frac{1}{3}[2.5i+2.5\hat{j}]$

$=\frac{5}{6}\hat{u}+\frac{5}{6}\hat{j}$