Question

Find the height of the center of mass of a semi-circular disk of radius $R=20\text{cm}$ from point $\text{O}$ (base center).

• A. $\frac{40}{3\pi }\text{cm}$
• B. $\frac{60}{3\pi }\text{cm}$
• C. $\frac{20}{3\pi }\text{cm}$
• D. $\frac{80}{3\pi }\text{cm}$

Answer 1

The correct option is D $\frac{80}{3\pi }\text{cm}$

Given, radius of semi-circular disk $R=20\text{cm}$.
Disk is symmetric about $y-$ axis. So $x-$ co-ordinate of center of mass of disk is zero.
We know, distance of $COM$ of semi-circular disk from center of base is $\frac{4R}{3\pi }$
Therefore, height of $COM$ of semi-circular disk from point $\text{O}=\frac{4R}{3\pi }$
$=\frac{4\times 20}{3\pi }\text{cm}$
$=\frac{80}{3\pi }\text{cm}$