Two light vertical springs with equal natural length and spring constants `k_(1)` and `k_(2)` are separated by a distance `l`. Their upper end the ends `A` and `B` of a light horizontal rod `AB`. A vertical downwards force `F` is applied at point `C` on the rod. `AB` will remain horizontal in equilibrium if the distance `AC` is

Options

A. `l/2`
B. `(lk_(1))/(k_(2)+k_(1))`
C. `(lk_(2))/(k_(1))`
D. `(lk_(2))/(k_(1)+k_(2))`

Answer

D

Explanation

AC=x
`x_(0)=ext^(0)`. In each spring
Torque about C
`K_(1)x_(0)x=K_(2)x_(0)(l-x)`
`x=(lk_(2))/(k_(1)+k_(2))`