A rod of length L is pivoted at one end and is rotated with as uniform angular velocity in a horizontal plane. Let `T_1 and T_2` be the tensions at the points L//4 and 3L//4 away from the pivoted ends.

Options

A. `T_(1)gtT_(2)`
B. `T_(2)gtT_(1)`
C. `T_(1)=T_(2)`
D. the realation between `T_(1)` and `T_(2)` depends on wheather the rod rotates clockwise or anticlockwise

Answer

A

Explanation

At `x=(L)(4),T_(1)=(1)/(2)(momega^(2))/(L)(L^(2)-(L^(2))/(4))`
`=(1)/(2)(momega^(2))/(L)xx(3L^(2))/(4)=(3momega^(2)L)/(8)`
`x=(3L)/(4),T_(2)=(1)/(2)(momega^(2))/(L)(L^(2)-(9L^(2))/(16))`
`=(1)/(2)(momega^(2))/(L).(7L^(2))/(16)=(7momega^(2)L)/(32)`
`T_(1)gtT_(2)`