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+1 vote
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in Physics by (150k points)
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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) T= T2

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

2 Answers

+3 votes
by (87.2k points) 1 flag
selected by
 
Best answer

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.

+1 vote
by (47.6k points)

Answer:(a) T1>T2

At L/4 from the pivoted end: 

Tension, T1 ​ = centrifugal force on the rod behind this point (of 3L/4 length)

At 3L/4 from the pivot end: 

Tension, T2 ​ = centrifugal force on the rod behind this point (of L/4 length)

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