Question

A drawing pin is pushed against a wooden table with a force of 10 N. The pressure exerted by the pin at a point on the table if an area of the point is $0.01c{m^2}$, is ${10^x}Pa$. Find $x$.

Answer 1

Hint: To solve this question, the definition of the pressure is essential to understand. The pressure is defined as the force applied to the body per unit area.
Pressure $P = \dfrac{F}{A}$
where $F$ = force in newtons (N), $A$ = area in metre-squares $\left( {{m^2}} \right)$.
The SI unit of pressure is N/${m^2}$ or pascal (Pa); however, there are several units of pressure used, commercially, such as psi (pounds per square inch) and cm or mm of mercury (for air pressure).

Complete step by step answer:
The SI unit of pressure is the pascal.
One pascal of pressure is said to be applied when a force of one newton is applied over a surface of one meter square.
$1Pa = \dfrac{{1N}}{{1{m^2}}}$
Consider a drawing pin being pushed into a wooden table.
Given, the force applied, $F = 10N$
Give, the area of the drawing pin, $A = 0.01c{m^2}$
To calculate the pressure in pascals, the force should be in the newton unit and the area should be in meter square.
Given area is in $c{m^2}$,
To convert $c{m^2}$ to ${m^2}$, we have to use the relation,
$1c{m^2} = {10^{ - 4}}{m^2}$
Given area, $A = 0.01c{m^2} = {10^{ - 2}}c{m^2}$
Converting to metre square, we have –
$\Rightarrow A = {10^{ - 2}} \times {10^{ - 4}} = {10^{ - 6}}{m^2}$
Now, we can calculate the pressure in pascals.
$\Rightarrow P = \dfrac{F}{A} = \dfrac{{10}}{{{{10}^{ - 6}}}} = {10^{1 + 6}} = {10^7}Pa$
The pressure, given in the question, is $P = {10^x}Pa$
Comparing the two, we get –
$10^x\,Pa = 10^7Pa$
$ \therefore x = 7 $
Thus, the value of $x = 7$.

Note:
Always take heed while converting the units of area. Students should remember that:
For converting a smaller unit like centi, milli etc. to metre, kilo, etc., we have to multiply by negative powers of 10.
Conversely, for converting a bigger unit like mega, kilo, meter etc. to centi, milli, etc., we have to multiply by positive powers of 10.