Broad, who will be replaced by Steven Finn for the match, which starts on Friday, faces a wait until next month's tour of India to play his 100th test match.
"Clearly we had the opportunity to not rotate, but the last thing we wanted was to go to India with too many people who haven't played much cricket," Cook told BBC Radio 5 live.
"We don't know a huge amount about either Batty or Ansari in terms of test cricket... but they will get one test each and that is important."
Slow left-armer Ansari, claimed 22 wickets in 10 matches for Surrey in the County Championship and will hope to form a potent bowling threat along with off-spinner Moeen Ali and leg-spinner Adil Rashid.
"One thing I've seen in the nets is he (Ansari) can bowl at good pace with good control," Cook said at the pre-match press conference. "It will be really interesting to see how he goes. He can also bat as well, which is good."
The 24-year-old Ansari was named in England's squad for the three-test series against Pakistan in the United Arab Emirates last year, but was injured hours after his first test call-up.
Cook told his pre-match press conference that fast bowler Jake Ball had also been in contention to replace Chris Woakes, who bowled just 14 overs in the first game.
"In an ideal way we would have liked Jake to have a game as well but we feel as if Chris Woakes hasn't played a huge amount of cricket on the subcontinent, didn't have a huge workload in the last game," he said.
"We feel it'll be beneficial for him to experience these conditions."
Traditionally, the Dhaka pitch has offered more for the batsmen than Chittagong, but Cook said he expects a similar challenge to the one they faced in the first test.
"You don't look too much into stats but historically Dhaka spins less than Chittagong," he added.
"I have a feeling that might not be the case in this game."
England squad for second Test: Alastair Cook (captain), Ben Duckett, Joe Root, Gary Ballance, Moeen Ali, Ben Stokes, Jonny Bairstow, Chris Woakes, Adil Rashid, Zafar Ansari, Steven Finn.
(Reporting by Nivedita Shankar in Bengaluru, editing by Simon Cambers)
