New York City Ballet principal dancer Sara Mearns and personal trainer Joel Prouty. Annie Wermiel/NY Post That babe next to you at the gym pumping hundred-pound barbells? She’s a ballerina, not a bodybuilder. These days, top dancers can’t get by on grace and agility alone — which is why more of them are hitting the gym after they leave the barre. As New York City Ballet principal dancer Sara Mearns and other stars have discovered, dead lifts and squats lead to better pirouettes and pliés. Cross-training, says Mearns’ trainer, Joel Prouty, can prevent injury and increase a dancer’s endurance and strength, improving performance during a rigorous career. But it’s still a fairly new concept. “There was no cross-training when I was a dancer,” Prouty tells The Post. “There was this fear that it would take away from the aesthetic” and cause a “bulky” look — “but it doesn’t have to.” Prouty, 39, performed with several ballet companies and toured with Twyla Tharp before retiring in ...