It is part of General Relativity that if you are in a (small) closed box, you cannot tell the difference between acceleration and a gravitational field.
I suppose you could argue that you would explain Earth's gravity to the occupants of the biosphere as a 1g acceleration away from the Earth for 50 years, a slow swivel of the spacecraft, and then deceleration at 1g for 50 years.
It is hard to say whether such a deception is possible without more details, but in principle it could be done if you have some way of obscuring the initial part of the journey - launch etc, where you would think some non-uniform acceleration would be inevitable.
There is also the question of how far you are going and whether there is a feasible propulsion system. An acceleration of 1g for only a year gets you up to relativistic speeds. You could easily travel to other galaxies in 50 years at this acceleration. So, if the destination was supposed to be a nearby star then the deception fails miserably, unless you try to convince the passengers that you are executing some sort of weird trajectory to get there.
Additionally, how big is the biosphere? What about tides due to the Sun and moon? Any sizeable body of water would show up tides (and indeed possibly the coriolis force due to the Earth's rotation).
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