A uniform rod of mass m, length L, area of cross-section A is rotated about an axis passing through one of it ends and perpendicular to its length with constant angular velocity w in a horizontal plane. If Y is the Young modulus of the material of rod, the increase in its length due to rotation ofrodis:

Options

A. `(m omega^(2) L^(2))/(AY)`
B. `(m omega^(2)L^(2))/(2 AY)`
C. `(m omega^(2)L^(2))/(3 AY)`
D. `( 2 m omega^(2)L^(2))/(AY)`

Answer

A

Explanation

`Y = ("stress")/("strain") = (F//A)/(Deltal //l) = (mr omega^(2)xxL)/(A xx Deltal) , Delta l = (m romega^(2) l)/(YA) , "if" r =l = (m omega^(2)L^(2))/(YA)`