Question

A 20 Pa pressure is applied on the head of a nail placed perpendicular to the surface of the wall. If the area of cross-section of the tip of the nail is$\dfrac{1}{{10}}$ times the area of cross section of the head, the pressure exerted at the wall is:
A. 10 Pa
B. 20 Pa
C. 200 Pa
D. None of these.

Answer 1

Hint:-
If the force applied is more than the area of the cross section then the applied pressure will be more and if the area of the cross section is very less than the applied force then also the pressure experienced will be more.
Formula used: The formula of pressure is given by,$P = \dfrac{F}{A}$ where P is the pressure F is the force applied on the body and A is the area of cross-section.

Complete step-by-step solution
It is given in the problem that a nail head is put a force of 20 Pa and the problem is asking us to find the value of pressure exerted at the wall by the nail and it is given that the area of the tip of nail is $\dfrac{1}{{10}}$ of the area of the head of the nail.
It is given that the pressure on the head of the nail is 20 Pa and the pressure on the nail head is given by,
$P = \dfrac{F}{A}$
Where P is the pressure F is the force applied on the body and A is the area of cross-section.
$ \Rightarrow 20 = \dfrac{F}{A}$ (as the pressure on the nail head is given by 20 Pa).
$ \Rightarrow F = 20 \cdot A$………eq. (1)
Now let us calculate the value of the pressure exerted by the nail on the wall.
$P = \dfrac{F}{A}$
Where P is the pressure F is the force applied on the body and A is the area of cross-section.
$ \Rightarrow {P_1} = \dfrac{F}{{{A_1}}}$
$ \Rightarrow {P_1} = \dfrac{F}{{\left( {\dfrac{A}{{10}}} \right)}}$
Replace the value of the force from the equation (1).
$ \Rightarrow {P_1} = \dfrac{{20 \cdot A}}{{\left( {\dfrac{A}{{10}}} \right)}}$
$ \Rightarrow {P_1} = 200Pa$.
The pressure exerted on the wall is equal to ${P_1} = 200Pa$. The correct option for this problem is option C.

Note:- In this problem it is given that a force is applied on a nail and they are asking us to find the value of the pressure experienced by the wall so here we should understand that the applied force here is not change but only the area of cross section will change when we consider the nail and when we consider the surface area of the tip of nail.