  In this article, we consider the projective bundle $\mathbb{P}_X(E)$ over a
smooth complex projective variety $X$, where $E$ is a semistable bundle on $X$
with $c_2(End(E)) =0$. We give a necessary and sufficient condition to get the
equality $ Nef^1\bigl(\mathbb{P}_X(E)\bigr) =
\overline{Eff}^1\bigl(\mathbb{P}_X(E)\bigr)$ of nef cone and pseudoeffective
cone of divisors in $\mathbb{P}_X(E)$. As an application of our result, we show
the equality of nef and pseudoeffective cones of divisors of projective bundles
over some special varieties. In particular, we show that weak Zariski
decomposition exists on these projective bundles. We also show that a
semistable bundle $E$ of rank $r \geq 2$ with $c_2\bigl(End(E)\bigr) = 0$ on a
smooth complex projective variety of Picard number 1 is $k$-homogeneous i.e.
$\overline{Eff}^k\bigl(\mathbb{P}_X(E)\bigr) =
Nef^k\bigl(\mathbb{P}_{X}(E)\bigr)$ for all $1 \leq k < r$. Finally, we show
that weak Zariski decomposition exists for a fibre product
$\mathbb{P}_C(E)\times_C\mathbb{P}(E')$ over a smooth projective curve $C$.
