Question

a uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity w about a vertical axis passing through one end. the tension in the rod at a distance x from the axis is?

Answer 1

 AB is a rod of length l ,mass M & this rod is rotating about end A....

now , mark a point c anywhere on the rod , distance bw end A & C is x ...

now the rod is divided into two parts , AC & CB .......

tension of rod at point C is (T)= dmw2r                   (dm is mass of part BC = m(l-x)/l )

                                          =M(l-x)w2r/l

this r is the distance of center of mass of BC from end A so r = (x+l)/2

so

           T = M(l-x)(l+x))w2 /2l    

          T = M(l2-x2)w2 /2l 

this is the expression for tension at any point

Answer 2

T=mw²(l²-x²)/2 ... Tension