Question

A rod of length L is hinged at one end and is rotated with constant angular velocity in horizontal plane.Let T₁ and T_{2 be tensions at L/4 and 3L/4 away from hinged end .....then
T1>T2
T1=T2
T1<T2}

Answer 1

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

^(W=omega)

For a point at 3L/4

T₂ = limit 3L/4 to L ∫ (mdx)w² x

=7/32 mw²L²

So T₁>T₂