Can a person inside a spaceship falling freely on a geodesic path, experience the same just like a person inside a car experience a force on a turn on earth i.e when the geodesic path is no more straight near a huge planet.
Little confused, this will only happen near a huge planet if the spaceship is large, because you mention tides on Earth due to moon and close to a black hole.One minor caveat to Orodruin's response - if the spaceship is large enough you will experience tidal forces. This would leave you pressed up against the side of the ship furthest or nearest the mass. Or, more uncomfortably, with one end of your body pressed against one side and the other end against the other.
This will only be a significant effect for a planet-sized ship (that's why we get tides on Earth) or very close to a small black hole.
In a curved spacetime, nearby geodesics are not quite exactly parallel ("geodesic deviation"), so nearby masses in free fall will want to move apart or be forced together. If the two masses are the opposite ends of some object, that object will experience crushing or stretching forces. The larger the volume of space we're considering, the greater the effect so it will be more pronounced inside a very large ship than a very small one.If so what is the role of a large ship in which one can experience a force on a turn due to spacetime curvature.
You always get tidal forces. In Newtonian terms, this is because the parts of the ship nearer the gravitating mass feel a stronger force than those further away. In GR terms, the reasoning is a bit different (geodesic deviation) but the effect is the same, at least qualitatively.Little confused, this will only happen near a huge planet if the spaceship is large, because you mention tides on Earth due to moon and close to a black hole.
 If so what is the role of a large ship in which one can experience a force on a turn due to spacetime curvature.