The Sanskrit grammatical tradition which has commenced with Panini's Astadhyayi mostly as a Padasastra has culminated as a Vakyasastra, at the hands of Bhartrhari. The grammarian-philosopher Bhartrhari and his authoritative work 'Vakyapadiya' have been a matter of study for modern scholars, at least for more than 50 years, since Ashok Aklujkar submitted his Ph.D. dissertation at Harvard University. The notions of a sentence and a word as a meaningful linguistic unit in the language have been a subject matter for the discussion in many works that followed later on. While some scholars have applied philological techniques to critically establish the text of the works of Bhartrhari, some others have devoted themselves to exploring philosophical insights from them. Some others have studied his works from the point of view of modern linguistics, and psychology. Few others have tried to justify the views by logical discussions. In this paper, we present a fresh view to study Bhartrhari, and his works, especially the 'Vakyapadiya'. This view is from the field of Natural Language Processing (NLP), more specifically, what is called as Cognitive NLP. We have studied the definitions of a sentence given by Bhartrhari at the beginning of the second chapter of 'Vakyapadiya'. We have researched one of these definitions by conducting an experiment and following the methodology of silent-reading of Sanskrit paragraphs. We collect the Gaze-behavior data of participants and analyze it to understand the underlying comprehension procedure in the human mind and present our results. We evaluate the statistical significance of our results using T-test, and discuss the caveats of our work. We also present some general remarks on this experiment and usefulness of this method for gaining more insights in the work of Bhartrhari.