Michael Clarke and Brad Haddin slammed tons before England lost Cook and were 35 for 1 at stumps in Adelaide.
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Skipper Michael Clarke (48*) and Brad Haddin (7*) were in the middle for Australia as hosts will aim for healthy first innings total on day two of the second Test.
On Day 1, a disciplined England attack shrugged off the challenge of a bland Adelaide Oval wicket to limit Australia to 273 for 5 and leave the second Ashes test delicately poised.
Chris Rogers (72) and Shane Watson (51) put on 121 for the second wicket before Jimmy Anderson and Graeme Swann struck five balls apart. Stuart Broad was picks of the bowlers as he claimed two wickets.