Question

find out the center of mass of a rod having uniformly distributed mass of M and length L lies at the middle point of rod.

Answer 1

Yes

By symmetry of shape and uniform of mass

Answer 2

Consider a rod of mass M and Lenth L.

let dx be a small part of the rod and its mass be dm.

s=M/L

so, dm= Mdx/L

Hence COM= integral of xdm/ integral of m

where x limits from 0 to L

com= 1/L   X [x^2 /2] limit from 0 to L

By solving We Get,

   COM=L/2

Hence COM Of a uniform rod of mass M and Length L lies at the middle point of rod.