As described, if the Pencil fell onto its tip, the transducer element (that sits immediately under the replaceable tip (as shown in your photo) may have suffered damage. The Pencil won't work at all unless the Pencil tip has been correctly fitted.
If the metal transducer element is intact and visually undamaged, you can try replacing the tip - ensuring that the replacement is screwed snugly into position; you should see a tiny gap, of about the thickness of a sheet of paper, between the tip and pencil body.
If replacing the pencil tip does not resolve this issue, or the tip is not correctly positioned in relation to the pencil body when fitted, then your Pencil is likely to have suffered irreparable damage.
As a diagnostic exercise, try pairing and testing the Pencil with another compatible iPad. Some retailers have display models of iPad that you can try-out the iPad - these offering an excellent opportunity to test the Pencil.
Otherwise, you would be best advised to visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to test both your iPad and Apple Pencil:
Genius Bar Reservation and Apple Support Options - Apple
While the standard AppleCare limited warranty does not cover accidental damage, if you have purchased the optional AppleCare+ cover for iPad at the same time as purchasing your ApplePencil, AppleCare+ coverage extends to providing cover for your Pencil - including accidental damage.
