A cat’s tail helps it in keeping balance. However, this does not mean that cats who lose their tails or are born without them cannot balance themselves. According to VetInfo, cats who suffer tail injuries that require amputation learn to balance without them. Nevertheless,
The primary purpose of your cat's tail is balance—it helps when walking out on a limb, and more importantly, it helps him flip in the air to land on his feet should he fall off that limb. On the other hand, cats don't need their whiskers to balance. As in all mammals, a cat's balance is controlled via the inner ear. The myth that cat whiskers affect balance may be related to the fact that cat whiskers are sensory organs.