Question

व्हाट इज द सेंटर ऑफ ग्रेविटी ऑफिस semi-circle ऑफ डायमीटर 12 सेंटीमीटर​

Answer 1

Step-by-step explanation:

To Find : Center of Gravity

Solution:

Diameter = 12 cm

Radius = 6 cm

Taking center at ( 0 , 0) and semicircle above x axis

Because of symmetry center of gravity will lie of y axis

A = (1/2)πr² = (1/2)π(6)² = 18π cm² ( area of semicircle)

x² + y² = r² = 6²

=> x² = (6² - y²)

=> x = √(36 - y²)

Let assume 36 - y² = z

=> -2ydy = dz

=> 2ydy = -dz

on substituting

on integrating

Applying limits 0 to 6

216/27π

= 8/π cm

= 2.5465 cm

Hence centre of gravity of a semi circle of diameter 12 cm

will be at a height of 8/π cm or 2.5465 cm from the center of Semicircle