Question

A rod of length L is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane. Let T1 and T2 be the tensions at the points L/4 and 3L/4 away from the pivoted ends.

(a) T1 > T2.

(b) T2 > T1.

(c) T1= T2.

(d) The relation between T1 and T2 depends on whether the rod rotates clockwise or anticlockwise.

Answer 1

The correct answer is (a) T1 > T2.

Explanation:

Taking the rod of uniform mass per unit length = m . Mass beyond a distance r from the pivot = m(L-r). And this mass will be assumed to be concentrated at middle of the (L-r) length ie at CG. So distance of the CG from the pivot = r+(L-r)/2=(L+r)/2. Force due to circular motion on this length = Tension at point r away from the pivot =m(L-r).ω² .(L+r)/2 =mω²(L²-r²)/2 It is clear from this expression that as r increases Tension in the rod decreases.