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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 tension at the points L/4 and 3L/4 always from the pivoted end. Then:

A
T1>T2
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B
T1=T2
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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 C T1>T2
Let mass per unit length of the rod is m
And take a strip of length dx at a distance x from the pivoted end
Tension in the rod is due to the centrifugal force in the part of the rod that is away from the point of interest
So, for the point at a distance L4

T1=LL/4(mdx)w2xdx

=1532mw2L2

For a point at 3L4

T2=L3L/4(mdx)w2xdx

=732mw2L2

So, T1>T2

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