व्हाट इज द सेंटर ऑफ ग्रेविटी ऑफिस semi-circle ऑफ डायमीटर 12 सेंटीमीटर
Answers
Answered by
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
Similar questions