Question

a plane lamina of radius 100 mm. find the centre of gravity lamina from the point o

Answer 1

As we know that,  a plane of the lamina of radius = 100 mm

is symmetrical to Y-Y axis bisecting the lamina, therefore its center of axis lies on-axis.

let O be the reffrence point .

Given r = 100 mm

To find the center of gravity lamina from the point O.

Assume that  α = 30°

$=\frac{\pi}{6} \mathrm{rad}$

$\bar{y}=\frac{2 r}{3} \frac{\sin \alpha}{\alpha}$

$\frac{2 \times 100}{3} \times \frac{\sin 30^{\circ}}{\left(\frac{\pi}{6}\right)}$

$\frac{200}{3}$ x $\frac{0.5}{\left(\frac{\pi}{6}\right)}$

= 66.66 mm

Hence, the centre of gravity lamina from the point o is $63.66$