Question

If a boy of mass 50 kg is sitting in a car accelerating with acceleration 0.5g on the road, then what is force applied by seat?
$
  {\text{A}}{\text{. 125N}} \\
  {\text{B}}{\text{. 250N}} \\
  {\text{C}}{\text{. 500N}} \\
  {\text{D}}{\text{. 175N}} \\
$

Answer 1

Hint: Normal reaction force is force exerted by a body on another body as a consequence of Newton's third law. This force is equal to the force exerted by one body on the other body given by Newton’s second law.

Detailed step by step solution:
Newton’s second law states that the external force exerted on a body is equal to the mass of the body and acceleration produced in that by the force. It is given as
$F = ma$
Here F represents the force exerted on the body, m is the mass of the given body while a represents the acceleration produced in the body due to the external force F.
Newton’s third law states that for every action on a body we get a reaction which is equal and opposite to the action. The normal reaction force is the force which comes into action as a consequence of this law. It is the force exerted one body on another when that body is subjected to a force. It is the force which does not allow the other body to pass across the body on which force is being applied.
We are given that a body is travelling in a car. The mass of boy is given as
$m = 50kg$
The car is accelerating and the magnitude of acceleration is given as
$a = 0.5g$ where $g = 10m/{s^2}$
Now the boy exerts the force on the seat due to his weight. He stays in the seat due to the normal reaction force exerted by the seat. This force is equal to the weight of the boy.
$\therefore F = mg = 50 \times 10 = 500N$
Hence, the correct answer is option C.

Note: The force exerted by the seat depends on the weight of the boy. It does not depend on the acceleration of the car. If we find the force exerted on the car then it will give answer to be option B which is wrong.