with its first $t$ frobenius pullbacks is semistable, then the induced $Gl(V)$-bundle is again semistable. This fact is crutial in their proof of boundedness of semistable $G$-bundles with fixed Chern classes. In this paper we give bounds for this $t$, in terms of certain numerical data attached to $G$ and $\rho$. The main ingedient of the proof is the use of the instability parabolic (also known sometimes as the Kempf’s parabolic) associated to points of the representing space (see \[Section 3\] for definition). The basic idea is as follows: Let $E$ be a principal $G$-bundle on $X$. Let $k(X)$ denote the function field of $X$. Let $E(G)$ be the group scheme associated to $E$ (see section 2 for definition). Let $E_{Gl(V)}$ denote the induced $Gl(V)$ bundle. Let $E(G)_\circ$ denote the generic fiber of $E(G)$. It is a group scheme defined over the function field of $X$. Let $P$ be any maximal parabolic in $Gl(V)$. Let $E(Gl(V)/P)$ be the associated $Gl(V)/P$ fiber-space. Again let $E(Gl(V)/P)_\circ$ denote the generic fiber of $E(Gl(V)/P)$. Then $E(G)_\circ$ acts on $E(Gl(V)/P)_\circ$ which is linearized by a suitable very ample line bundle. If $E_{Gl(V)}$ admits a reduction of structure group to this maximal parabolic $P$, then we 