Question

In the given arrangement, the normal force applied by block on the ground is:

A) $mg$
B) $mg - f\cos \theta$
C) $mg + f\cos \theta$
D) $F\cos \theta$

Answer 1

In this question, resolve the force components of the blocks in its vertical and horizontal components then find the Normal force acting and the force acting on the ground and balance the two forces.

Complete step by step solution:
In the question, it is given that a block is placed at the ground, the angle at which the force $F$ is acting is given as $\theta$. The mass of the block is given as $m$.

Now let us consider the above figure. According to the component’s resolution of forces in a block, the horizontal force distribution is given by $F\sin \theta$ and the vertical force distribution is given by $F\cos \theta$.
Now the force that the block is imposing on the ground is given by $mg$ (Force acting in the ground due to gravitation and the block).
Now, the definition of Normal Force states that- The normal force is the support force exerted upon an object that is in contact with another stable object. For example, a book is kept on a surface, then the surface will exert an upward force on the book for supporting the weight of the book. On occasions, a normal force is exerted horizontally between two objects that are in contact with each other. For instance, if a person leans against a wall, the wall pushes horizontally on the person.
So, in upward direction normal force $N$ is acting.
Now by balancing the upward and downward force of the block, we get:
$\Rightarrow N + F\cos \theta = mg$
So, from the above equation we can write, the Normal force applied by the block in the ground is given by:
$N = mg - F\cos \theta$

So, the correct answer is option (B).

Note: While solving such type of questions ensure the direction of the components of the forces as take the sign convention as, if the force is in vertical upward direction take it as position, if the force is in vertical downward direction take it as negative, if the force is in horizontally right direction take it as positive and if it is in horizontally left direction take it as negative.