At the break, Cook was unbeaten on 56 with in-form Gary Ballance undefeated on 40 in an unbroken 82-run stand for the second wicket after Varun Aaron had removed opener Sam Robson (37) early in the day.
While Cook had six fours in 140 balls, fellow left-hander Ballance was more attacking having eight hits to the fence in 66 balls.
The Indian bowlers toiled hard but the conditions had changed quite a bit from the first day.
Bhuvneshwar Kumar (0-37), Varun Aaron (1-49), Ishant Sharma (0-23) and Stuart Binny (0-22) were all deployed to make use of a semi-new ball but only the one wicket was all that came through in the session. Ravichandran Ashwin (0-9) also bowled four overs.
The day started with England at 62/0 overnight, trailing only by 86 runs. India needed early breakthroughs to force the hosts onto the backfoot with Kumar starting proceedings.
And they did get a bright spark when in the second over of the day 21st of the innings Aaron bowled Sam Robson with quick straight delivery that beat the batsman.
The under-fire opening batsman scored 37 runs off 70 balls, including 6 boundaries, and added 66 runs for the first wicket with Cook.
It brought Ballance to the crease but he was quick to get off the mark and got a nice start first up to dash any hopes the Indians had of triggering a sudden collapse.