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Example: In class, when a teacher proposes some unreasonable assignment, students hesitate to express their objection until someone steps-up and then others find courage to talk.
I've tried searching for the term for this phenomenon but I don't know what I'm looking for exactly.
One related term I found is the bandwagon effect.
In layman’s term the bandwagon effect refers to people doing certain things because other people are doing them, regardless of their own beliefs, which they may ignore or override.
The general rule is that conduct or beliefs spread among people, as fads and trends clearly do, with "the probability of any individual adopting it increasing with the proportion who have already done so". (Colman, Andrew 2003) As more people come to believe in something, others also "hop on the bandwagon" regardless of the underlying evidence.
Colman, Andrew (2003). Oxford Dictionary of Psychology. New York: Oxford University Press. p. 77. ISBN 0-19-280632-7.
Your example of no student willing to object until one objects is analagous to Asch's conformity experiments. To quote the Wikipedia article:
In a control group, with no pressure to conform to an erroneous view, only one participant out of 35 ever gave an incorrect answer. Solomon Asch hypothesized that the majority of participants would not conform to something obviously wrong; however, when surrounded by individuals all voicing an incorrect answer, participants provided incorrect responses on a high proportion of the questions (32%). Seventy-five percent of the participants gave an incorrect answer to at least one question. ...
The unanimity of the confederates has also been varied. When the confederates are not unanimous in their judgment, even if only one confederate voices a different opinion, participants are much more likely to resist the urge to conform (only 5–10% conform) than when the confederates all agree.
