Question

a chain of 100 links us 1m long and has a mass of 2kg .with the ends fastened together it isw set rotating at 3000rpm,in a horizontal plane.the centripetal force on each link is?

Answer 1

The entire chain is along the radius of the circle in which it is rotating in a horizontal circle.

     Length of each link = a = 1 m / 100 = 1 cm
       mass of each link = m = 2 kg /100 = 0.02 kg

Let us consider 'n' th link from the center of circle. It is revolving in a circle of radius  R = length of (n-1) links and 1/2 of length of nth link.
              = (n - 1) 1 cm + 1/2 cm  = (n - 1/2) /100  metes

average centripetal force on the nth link =  m R ω² , 
         where m = mass of link,  R = distance of nth link from center,  ω = angular velocity

              = 0.02 * (n - 1/2) /100 * (2π 3000/60)²  newtons
              =  2π² (n - 1/2)  Newtons

   So average centripetal force on the center of mass of first link is :  π² Newtons
       on the 2nd link  is  3 π².    It increases by 2π² for each link.