Question

A man of weight $mg$ is moving upward in a rocket with acceleration $4g$. His apparent weight inside the rocket will be?
A. zero
B. $4mg$
C. $5mg$
D. $2mg$

Answer 1

Use the relation between the apparent weight of the man and the normal force exerted by the rocket on the man. Determine the total acceleration of the man-rocket system and calculate the apparent weight of the man.

Formula used:
The equation for the weight $W$ of an object is
$W = mg$ …… (1)
Here, $m$ is the mass of the object and $g$ is the acceleration due to gravity.
The normal $N$ force exerted by a surface on the object in its contact is given by
$N = mg$ …… (2)
Here, $m$ is the mass of the object and $g$ is the acceleration due to gravity.

Complete step by step answer:
The weight $W$ of the man moving in the rocket is $mg$.
$W = mg$
From the above equation (1), it can be concluded that the mass of the man is $m$.
The acceleration of the rocket is $4g$.
$a = 4g$
The apparent weight of the man is equal to the normal force exerted by the rocket on the man.
The formula for normal force exerted by the rocket on the man includes the acceleration. Hence, determine the total acceleration of the system of man and rocket.
The total acceleration $a$ of the system is the sum of the acceleration of the rocket $4g$ and the acceleration of the man $g$.
$a = 4g + g$
$\Rightarrow a = 5g$
Hence, the total acceleration of the system is $5g$.
Calculate the normal force exerted by the rocket on the man.
Rewrite equation (1) for the normal force exerted by the rocket on the man.
$N = ma$
Substitute $5g$ for $a$ in the above equation.
$N = m\left( {5g} \right)$
$\therefore N = 5mg$
Hence, the normal force exerted by the rocket on the man is $5mg$.

Therefore, the apparent weight of the man is $5mg$.

So, the correct answer is “Option C”.

Note:
The man will feel heavier when the rocket is moving in the upward direction as the apparent weight of the man is more than the actual weight of the man.
The apparent weight of the man is equal to the normal force exerted by the rocket on the man.