I think perhaps you should clarify the birthplace of the industrial revolution question......Are you referring to the American Industrial revolution, or the UK one? If it is the UK one....surely it is Ironbridge, whereas Manchester is considered the "powerhouse" of the revolution, not the birthplace (imo)
Indeed - I knew there was a Manchester in NH, but that couldn't be right as the English city never is referred to as the 'birthplace'. I tried Ironbridge and Telford (whose signs declare it, due to Ironbridge now being inside its borders) which market themselves on this claim, before trying Manchester just because I assumed that the quiz author had done the research.
I've never heard Manchester was the birthplace of the industrial revolution (source?). In primary school, we were taught it started in a place called Ironbridge, but deeper research suggests that the Industrial Revolution didn't start in any one specific town or city, but rather all over England, as a result of cultural and economic changes.
"The Iron Bridge's story began in the early 18th century, in the nearby village of Coalbrookdale. Abraham Darby pioneered the smelting of iron using coke, a process that was a catalyst for the Industrial Revolution. It was Abraham Darby III who cast the ironwork for the bridge that still stands today, using the same techniques developed by his grandfather." Source: https://www.english-heritage.org.uk/visit/places/iron-bridge/