Question

If the force on the surface is doubled and the area is reduced to half, pressure will
A. become 2 times
B. become 3 times
C. become 4 times
D. remains unchanged

Answer 1

Hint Pressure depends on two factors: first one is Force applied and second one is Area over which force acts. Pressure is directly proportional to the Force (F) and inversely proportional to the area (A) when other quantities are kept constant. So, when Area A is doubled pressure is halved. Area A is halved Pressure P is doubled.

Solution
Initially force is F
F force on the surface is doubled
Now new force become Fnew
$F_{new}$ =2F
Initially area is A
Area is reduced to half
Now new area become $A_{new}$
$A_{new}$= $\dfrac{A}{2}$
The elementary mathematical expression for pressure is given by:
pressure=$\dfrac{Force}{Area}$? = $\dfrac{F}{A}$?
Now new force become
$P_{new}$= $\dfrac{F_{new}}{A_{new}}$
Putting the value and we get
=4P

So pressure will become 4 times.

Note: Pressure is defined as force acting on a unit area of the object. Pressure is a scalar quantity. In SI units, the unit of pressure is the Pascal (Pa). Any item that possesses weight, whether or not at rest or not, exerts a strain upon the surface with which it is in touch. The magnitude of the pressure exerted with the aid of an item on a given surface is identical to its weight performing within the course perpendicular to that surface, divided by using the whole floor vicinity of contact between the object and the floor. indicates the graphical representations and corresponding mathematical expressions for the case in which a force acts perpendicular to the surface of touch, in addition to the case in which a force acts at perspective θ relative to the floor.