Question

show that the centre of mass of a uniform rod of mass M and length L lies at the middle point of the rod

please provide photo of the solution clearly as possible

Answer 1

Let l= length of rod

m= mass of the rod.

Let consider one end of the rod to be origin i.e (0,0) and henceforth the other end will lie at ( l,0) when placed along x- axis.

Let at x distance from the origin dm mass is of rod element of length dx. (i.e very small mass of rod )

Mass per unit lenght = m/l

Then small mass dm (of lenght dx)= m.dx/l

Center of mass = ∫x.dm/m

=∫ x . m.dx/m.l

= ∫ x.dx/l

= [x^2/2] /l ( limits from 0 to l )

= l^2/2l

= l/2

Hence Proved.

by irfan