Question

why a long spanner is used to tighten a nut

Answer 1

Foe a long spanner , the handle with distance 'd' is large.we know moment of force is equal to force × distance.The turning effect of force is nothing but moment of force.
So it is easier to rotate the objct (nut).
Hence, long spanner is used to rotate nut.

Answer 2

Because the longer the spanner is , the more is the perpendicular distance between the axis of spanner through which it rotates and the distance of your hand. And when perpendicular distance is more, less force is required. Try using the spanner by holding it with ur hand kept near the nut.