Question

A pressure of 10 Pa acts on an area of 3.0msquare. What is the force acting on the area? What force willbe exerted by the application of same pressure if the area is made one third

Answer 1

$<b><u><i> Hey mate!! Here's your answer</i></u></b>$
______________________________

$\huge{Given-}$

A pressure (P) of 10 Pa acts on an area of 3 m².

$\huge{To\: Find}$

(1) The force (F) acting on the area.

(2) Force exerted when same pressure acts on one-third of the original area.

$\huge{Solution-}$

$<b>Firstly, Pressure(P) is the force(F) acting on an unit area(A). The formula to find pressure = force/area, and it's unit is N/m² or Pa(Pascal). Also, pressure is directly proportional to the force acting and inversely proportional to the surface area. </b>$

$<u>Coming back to the question</u>$

$\mathcal{In \: first\: case}$

P = 10 Pa
Area = 3 m²

Now,

P = F/A

=> F = PA (by cross multiplying)

=> F = 10 × 3

=> F = 30 N (where N = Newton)

Hence, Force acting on an area of 3 m² which exerts a pressure of 10 Pa in 30 N

$\mathcal{Now, \: in\: second\: case}$

P = 10 Pa

A = 1/3 of 3 = 1 m²

Now,

F = PA

= 10 × 1

= 10 N

Hence, Force acting on an area of 1 m² which exerts a pressure of 10 Pa is 10 N.

$\blue{\mathfrak{Finally,}}$

Your answers are,

$\mathcal{\boxed{\red{(1) \: = \: 30\: N}}}$
$\mathcal{\boxed{\pink{(2)\: = \: 10\: N}}}$
______________________________

$\mathcal{\huge{\bold{\green{Thank\: you}}}}$