Question

What is the normal reaction of the body when it is at rest on (1) a horizontal surface
(2) an inclined surface?

Answer 1

Answer:

1. $N=W=mg$
2. $N=mgsin\theta$

Explanation:

1. When the body is at rest on a horizontal surface:

The normal reaction of the body is equal to the weight of the body.

From third law of motion: we know that every force has equal and opposite reaction. Thus the normal reaction of the body is equal to the weight of the body.

$N=W=mg$

2. When the body is at rest on a inclined surface :

Let us assume :

$\theta\ is\ the\ angle\ made\ by\ the\ inclined\ surface\ with\ the\ horizontal$

The components of the gravitational force acting on the body is

$mgcos\theta$ in the direction of the inclined surface and $mgsin\theta$ in the direction perpendicular to the inclined plane .

$mgsin\theta$ is the force acting perpendicular to the inclined surface which is equal to the  normal reaction of the body.

$N=mgsin\theta$

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Answer 2

Reaction of the body when it is at rest on

(1) a horizontal surface $N=W=mg$

(2) an inclined surface $N=mgsin$θ

Explanation:

1. When the body is at rest on a horizontal surface:

The weight of the body is equal to the normal reaction of the body.  

From third law of motion:  "Every force has equal and opposite reaction". Thus The weight of the body is equal to the normal reaction of the body

Reaction of the body when it is at rest on horizontal surface $N=W=mg$

2. When the body is at rest on a inclined surface :

Let  θ is the angle made by the inclined surface with the horizontal surface.When we consider the components of the gravitational force which is acting on the body and they are in the direction of the inclined surface and are in the direction which is perpendicular to the inclined plane .

$N=mgsin$θ

So  the force which is acting upon is perpendicular to the inclined surface and that is equal to the  normal reaction of the body.

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