Question

A man of mass $90{\text{ kg}}$ is standing in an elevator whose cable broke suddenly. If the elevator falls freely, the force exerted by the floor on the man is
A. $90{\text{ N}}$
B. $180{\text{ N}}$
C. $0{\text{ N}}$
D. ${\text{Any negative value}}$

Answer 1

Hint Whenever an object falls freely, its acceleration will be equal to the acceleration due to gravity $g$. A pseudo force is acting on the man in this case which is the actual weight of the man. The force exerted by the floor of the elevator will be the difference of the actual weight of the man and the upward force acting on it.

Complete step by step answer
When a body drops from a height its initial velocity is zero so it moves downward only because of the acceleration due to gravity. The body moves due to the only force acting on it i.e. gravitational force. This type of motion is known as Free Fall motion.
As given in the question, the mass of man $m = 90{\text{ kg}}$ .
Now if the elevator falls the downward acceleration of the man in the elevator will be $a = g$ and a pseudo force acts on the man in this case which is the actual weight of the man.
Now, the force exerted by the floor of the elevator will be the difference of the actual weight of the man and the upward force acting on it i.e.
\[{\text{Force exerted by the floor }} = {\text{ }}ma - mg = mg - mg = 0N\]
Therefore, the force exerted by the floor on the man is zero.

Hence, option C is correct.

Note Pseudo force is a force that appears to act on a body whose motion is observed by a non-inertial frame of reference, such as an accelerating or rotating reference frame. This force is also known as fictitious force or d’Alembert force.