Consider a body in an elevator moving down with some acceleration, say . The tension in the string ‘T’ is given by,
T =mg – ma
When the body is falling freely, then, a = g, the acceleration due to gravity.
Substituting a = g in the above equation,
T = mg – mg = 0
Tension ‘T’ read by the scale, gives the apparent weight of the body. Therefore, the apparent weight of the body will be zero. Hence, a body becomes weightless when the elevator falls freely under the action of gravitational force.