The elongation in a metallic rod hinged at one end and rotating in a horizontal plane becomes four times of the intial value. The angular velocity of ratation becomes

Options

A. two times the initial value
B. half of initial value
C. one third of initial value
D. four times the initial value

Answer

A

Explanation

`-int_T^0triangleT=int_0^l(m)/(l)dxomega^2x impliesT=(m)/(l)omega^2(x^2)/(2)`
`impliesY=(Fl)/(Atrianglel)trianglel=(Fl)/(Ay)`
`trianglel=((m)/(l)(omega^2x^2)/(2)dx)/(AY)trianglel=(m)/(l)(omega^2l^3)/(6AY)trianglel=(rhoomega^2l^3)/(6y)`
`trianglel=omega^2`
`omega^2=2omega_1`