Question

Why do we weigh weightless when the lift falls down when it's cord is cut?

Answer 1

When someone is standing on a still surface or a surface under uniform motion, the weight is balanced by the reaction of the surface. This reactionary force gives the feeling of weight.

When we fall along with the lift, acceleration of both lift and our body is same. So relatively, lift doesn't apply force on our body as it cannot cause acceleration.

So, we feel weightless.

In more advanced words,

As we know that, during free fall the only force acting is a man's weight itself. So, both lift and the boy inside would be in a state of free fall and hence the normal contact force between the floor of the lift and the man would be zero. Therefore boy would experience weightlessness.