INBOARD R MAIN TIRE BLEW OUT ON A DC9-50 DURING TKOF RESULTING IN THE FLC DECLARING AN EMER FOR LNDG AT THEIR DEST IN ORDER TO HAVE EMER EQUIP STANDING BY JUST IN CASE OF TROUBLE.

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ON TKOF RWY 12R; RIGHT AT V1; NOTICED A RUMBLING FROM THE MAIN GEAR ON ROTATION (VR). THE RUMBLING SOUND GOT LOUDER. SUSPECTED A BLOWN TIRE. SAT TWR CONFIRMED DEBRIS ON RWY. FLT WAS CONTINUED TO STL. AN EMER WAS DECLARED; A TWR FLY-BY WAS MADE; AND LNDG MADE WITH EMER EQUIP STANDING BY. THE LNDG WAS UNEVENTFUL. DAMAGE TO INBOARD R MAIN TIRE; R INBOARD TRAILING EDGE FLAP. SUPPLEMENTAL INFO FROM ACN 400421: WE DID NOTICE A SLIGHT SMELL OF 'BURNED RUBBER' IN THE AIRPLANE; BUT ONLY FOR A FEW SECONDS. THE CAPT DECLARED AN EMER; BRIEFED THE FLT ATTENDANTS; AND INFORMED THE PAX WHAT WAS HAPPENING. WE DID A FLY-BY AT STL ARPT (RWY 30L); TO SEE IF STL TWR COULD VERIFY THE CONDITION OF OUR LNDG GEAR. THEY COULD NOT VERIFY OUR CONDITION BECAUSE IT WAS TOO DARK. THE STL FIRE DEPT CHKED OUR LNDG GEAR AND FOUND NO EVIDENCE OF SMOKE OR FIRE. THE ACFT WAS TOWED TO THE GATE AND THE PAX WERE DEPLANED. THE CAPT AND I THEN LOOKED AT THE AIRPLANE. THE R-HAND INBOARD TIRE HAD BLOWN AND WAS MISSING ITS RECAP OUTER PORTION.