Question

A man of mass $m$ in an elevator moving downward with an acceleration $\dfrac{g}{5}$. The force exerted by the bottom surface of the elevator on the man will be:
A) $\dfrac{{4mg}}{5}$
B) $\dfrac{{6mg}}{5}$
C) $\dfrac{{2mg}}{5}$
D) $\dfrac{{mg}}{5}$

Answer 1

In order to answer the given question, first of all we need to find the forces that are acting on the man. Accordingly, we need to relate the forces acting on the man and then solve it to get the required solution.

Complete step by step solution:
First of all let us find the forces that are acting on the man.
First of all the gravitational force with which the man is pulled down is acting on the man. This force is given by, $mg$.
Since, the elevator is accelerating a pseudo force will be acting on the man in upward direction. This force is given by $ma$.
Also, a normal reaction force will be acting in an upward direction which we need to find.
Now, we know that the action force will be equal to the reaction force.
So, we can write the equation as,
$\Rightarrow F = mg - ma$……………….. (i)
The value of acceleration in the question is given as$\dfrac{g}{5}$.
So, putting the values in the equation (i), we get,
$\Rightarrow F = mg - \dfrac{{mg}}{5}$
$\Rightarrow F = \dfrac{{5mg - mg}}{5} = \dfrac{{4mg}}{5}$
Therefore, the required value of the force exerted by the bottom surface of the elevator on the man is $\dfrac{{4mg}}{5}$.

Hence, option (A), i.e. $\dfrac{{4mg}}{5}$ is the correct choice for the given question.

Note: The force which continuously acts downwards on a body due to gravity is known as the gravitational force which is actually the weight of a body. To balance an external force acting on a body, the gravitational force always acts in the downward direction. This force is also known as gravitational pull.