Let $X\subset\mathbb{P}^n$ be a **smooth** projective variety of dimension $\geq 2$ and assume that it is not contained in any hyperplane. Now, take some hyperplane $H\subset\mathbb{P}^n$ and consider the set $X\cap H$. Is it possible that there exists another hyperplane $H'$ containing the set $X\cap H$ **if we assume furthermore that $X\cap H$ does not contain ruled components?**

**EDIT1:** As @Lev Borisov pointed out in his answer, such examples exist if we don't put any restrictions on the geometry of the intersection set.

**EDIT2:** The example can be generalized in such a way that the set $X\cap H$ is almost arbitrary. So the assumption about ruled components does not make any difference.