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. Then:

A
T1>T2
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B
T2>T1
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C
T1=T2
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D
the relation between T1 and T2 depends on whether the rod rotates clockwise or anticlockwise
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Solution

The correct option is A T1>T2At L/4 from the pivoted end:Tension, T1= centrifugal force on the rod behind this point (of 3L/4 length)⇒ T1=m′ω2r=ML34Lω2(L4+3L8) (because r is the distance of COM)⇒ T1=1532Mω2LAt 3L/4 from the pivot end:Tension, T2= centrifugal force on the rod behind this point (of L/4 length)⇒ T2=m′ω2r=ML14Lω2(3L4+L8) (because r is distance of COM)⇒ T2=732Mω2L∴ T1>T2

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