I am being blackmailed for financial benefits by a girl

I was on an adult webcam chat site for a brief duration. Whilst on the site, one of the webcam viewers requested me to remove my undergarment, which I did for a second and wore it back. She told me that she wanted to be in touch and took my mobile number. I was foolish enough to even give her so. The following day, she messaged me on whatsapp, sending me a recording of this act and screenshots of my facebook friends, threatening me to upload this video on adult sites and sending it across to my family and friends through facebook. She demanded an amount of INR 60.000 for deleting this video and not sharing it with anyone. I am a Chartered Accountant by profession and to the best of my knowledge, being an adult, I have not performed an act that would construe to be illegal or immoral or punishable under IPC or otherwise. I did not record any act with any girl online. I would request your advice on how to go about this situation. I have her number but I have blocked it. I would not want to face a humiliation and embarrassment and yet I would like to stop her from blackmailing not just me, but anyone else. If I go to the police, am I likely to be harassed by them? Also, I have saved the entire conversation as evidence towards future courses of action against her. What are the cops likely to do if I lodge a formal written complaint and what would be my rights? Again, bearing in mind that I would not want any public humiliation or embarrassment? Request your advice on my situation.