Can wife put rape case on husband? What to do, FIR filed against him?

As we can see, in our opinion your relative should try and settle the matter with his wife, however if the same fails, he should follow the following steps to ensure that he is able to get acquitted of the false charges:

STEP - I: Safeguard himself

He should try and collect evidence to prove that the marriage was not working. It may include any recordings, mails, any third party mediator who had tried to settle their disputes, etc. This is basically to prove that the said allegations are baseless and only to harass the husband.

STEP - II: Intimating/Complaining the Police:

He should intimate the nearest Police Station about the facts of his case in writing stating that he is ready to fully co-operate with the Police with the investigation and that the said allegations are baseless.

He can even write a complaint to the nearest police station, detailing about blackmailing, her false allegations and her unscrupulous behaviour.  

STEP - III: Thereafter file a petition for divorce under Section 13 of the Hindu Marriage Act

Section 13 of the Act has been reproduced below for your better understanding.

Section 13(1) states that a petition may be presented by either the husband or the wife, for dissolution of marriage by a decree of divorce on the ground that the other party-

i. has, after the solemnization of the marriage, had voluntary, sexual intercourse with any person other than his or her spouse; or

a. has, after the solemnization of the marriage, treated the petitioner with cruelty; or

b. has deserted the petitioner for a continuous period of not less than two years immediately preceding the presentation of the petition; or

ii. has ceased to be a Hindu by conversion to another religion; or

iii. has been incurably of unsound mind, or has been suffering continuously or intermittently from mental disorder of such a kind and to such an extent that the petitioner cannot reasonably be expected to live with the respondent. Explanation.- In this clause,-

a. the expression" mental disorder" means mental illness, arrested or incomplete development of mind, psychopathic disorder or any other disorder or disability of mind and includes schizophrenia;

b. the expression" psychopathic disorder" means a persistent disorder or disability of mind (whether or not including sub- normality of intelligence) which results in abnormally aggressive or seriously irresponsible conduct on the part of the other party, and whether or not it require or is susceptible to medical treatment; or

iv. has been suffering from a virulent and incurable from of leprosy; or

v. has been suffering from venereal disease in a communicable from; or

vi. has renounced the world by entering any religious order; or

vii. has not been heard of as being alive for a period of seven years or more by those persons who would naturally have heard of it, had that party been alive.

Your relative's situation can fit under Section 13(1)(ia). The term cruelty includes mental as well as physical cruelty. 

Therefore your relative can file a petition seeking Divorce. The Court shall depend upon the facts of the case grant the divorce and decides the alimony or maintenance which he shall be liable to pay to his wife.