We consider a generalized Randall Sundrum (RS) brane world scenario with a cosmological constant
induced on the visible brane. We show that for
, resolution of the hierarchy problem requires an upper bound on the magnitude of
. The corresponding tension on the visible brane can be positive or negative. On the other hand, there is no such bound for
. However,
... [Show full abstract] in this case, the resolution of the hierarchy problem along with the tuning of the value of the cosmological constant to its observed value closed to (in Planck units) naturally lead to the tuning of the modulus to a small value of inverse Planck length as estimated in the original RS scenario.