Authenticity of Sanskrit Verses containing the word "HINDU"

Question

We all know that the word Hindu is a Persian word for the Sindu river and was later used to refer to the region to other side of the Sindu river as Hindustan which then became India. But this page says there are some people who try to justify the word "Hindu" was used by Rishis several thousand years ago by citing this verse:

Aaasindo Sindhu Paryantham Yasyabharatha Bhoomikah

Mathrubhuh Pithrubhoochaiva sah Vai Hindurithismrithaah

Rough Translation: Whoever considers the land of Bharatha Bhoomi between Sapta Sindu and the Indian Ocean as his or her motherland and fatherland is known as Hindu.

The above verse is said to be from Vishnu Purana, Padma Purana and the Bruhaspati Samhita.

Is the verse authentic or this verse just interpolation?

Answer 1

The verse you cited though slightly different from the original appears to be authored by Vinayak Damodar Savarkar a.k.a Veer Savarkar.

From the preface to Hindutva: Who is a Hindu? by Savarkar:

It was on the white-washed walls of his solitary cell in the Andamanees prison that the first outlines of this book were sketched, chapters and points fixed and the definition versified.

A gifted poet as Savarkarji was he framed the definition into the following fine couplet...

आसिंधु सिंधु-पर्यन्ता यस्य भारत-भूमिका ।
पितृभूः पुण्यभूश्चैव स वै हिंदुरिति स्मृतः ॥

It is as melodious and pleasing to the ear as it is convincing in its inexorable logic to the intellect. Its wording is redolent with an appeal to the dearest and holiest traditions of the Hindu race. It has caught up the incomprehensible diversity and dimensions of a people some thirty crores in count in the two magical words 'पितृभू' and 'पुण्यभू' — the identity of the Fatherland with the Holyland.

This couplet has now come to exercise the authority of a quotation from holy scriptures. Large sections of the Hindu public have actually been inquiring every now and then the name of the Smriti and Puran from which this couplet is quoted. The Hindu Mahasabha and the Hindudom in general from Kashmir to Rameshwar have enthusiastically acknowledged it as the best possible definition of the Hindu-Nation — 'हिंदुराष्ट्र.'

Answer 2

In olden days there was no concept as other religions. so it was not necessary to give a name to hinduism. it was only called SANATAN dharm or only dharm back then. so this verse is not genuine