Determine the zcoordinate of the mass center of the body con

Determine the z-coordinate of the mass center of the body constructed of uniform slender rod.

Solution

>> Let\'s divide the whole body into two parts :

1). Diameter, Its Center of Mass will lie at O point

2). Semicircular ring, Its Z- Coordinate of center of mass lies at (2r/)

>> Now, As Mass = Volume*Density = Area*Length*Density

As, Cross Section Area and Density are same for both parts

while, L1 = Length of 1st part = 2r

L2 = Length of 2nd Part = r

So, m1/L1 = m2/L2

=> m1/(2r) = m2/(r)

=> m2 = (m1)(/2)

>> Now, Let z = Overall Center of Mass of Body

=> (m1 + m2)z = m1*z1 + m2*z2

=> (m2)*(1 + 2/)z = 0 + (m2)*2r/

=> z = (2/( + 2)) r

or, z = 0.389*r ......ANSWER.....