Question

Find the distance of the center of mass from the geometric center for a uniform thin semi-circular disc of radius R=3π meters.

Answer 1

Answer:

Explanation:As the wire is uniform, the mass per unit length of the wire is

πR

M

. The mass of the element is, therefore,

dm=(

πR

M

)(Rdθ)=

π

M

dθ

The coordinates of the center of mass are

X=

M

1

∫xdm=

M

1

∫

0

π

(Rcosθ)(

π

M

)dθ=0

Y=

M

1

∫ydm=

M

1

∫

0

π

(Rsinθ)(

π

M

)dθ=

π

2R

Hence, position of center of mass, (0,

π

2R

)