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) T1 c) T1 = T2

Answer 1

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

 

Answer 2

Answer:

t1>t2

Explanation:

by integration of mw^2r