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A rod of length L is pivoted at one end and is rotated witha uniform angular velocity in a horizontal plane.Let T 1 and T 2 be the tnesion at the points L/4 and 3L/4 away from the pivoted ends A.T 2 > T 1 B.T 1 >T 2 Ans- B

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


A.T2 > T1        B.T1>T2


Ans- B

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear manoj

let mass per unit length of rod is m

and take a strip of lenghth dx at a distance x from the pivoted end

tension in rod is due to centrifugal force in part of rod that is away from the point of interest

so for point at a distance L/4

 

T1  = limit  L/4 to L    ∫ (mdx)w2 x

     =15/32 mw2L2

 

For a point at 3L/4

T2  = limit  3L/4 to L    ∫ (mdx)w2 x

      =7/32 mw2L2

 

So  T1>T2

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Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

let mass per unit length of rod is m
and take a strip of lenghth dx at a distance x from the pivoted end
tension in rod is due to centrifugal force in part of rod that is away from the point of interest
so for point at a distance L/4
T1 = limit L/4 to L ∫ (mdx)w2 x
=15/32 mw2L2
For a point at 3L/4
T2 = limit 3L/4 to L ∫ (mdx)w2 x
=7/32 mw2L2
So T1>T2

Thanks and Regards

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