Question

Calculate the greatest and the least pressure exerted by a metal block of size \[20cm{\text{ }} \times 8cm \times 5cm\] and having mass \[5kg\]. Take \[g = 10/{s^2}\].
1) \[12500pa{\text{ }};{\text{ }}3125pa\]
2) \[11500pa{\text{ }};{\text{ }}3125pa\;\]
3)\[13500pa{\text{ }};{\text{ }}5125pa\]
4) \[12500pa;{\text{ }}5125pa\]

Answer 1

Hint:-Find the value of force by given value of\[g = 10/{s^2}\], pressure is inversely proportional to the area of cross-section. We can apply Pascal law to greatest and least pressure.

Formula used:-Pressure is defined through the equation:
 $P = \dfrac{F}{A}$
Where F is the force in Newton, P is the pressure in Pascal and A is the area in \[{m^2}\].

Complete step by step answer: So, we got rectangular block with dimensions 20cm by 8cm by 5cm, or if we write this in meters, it is \[0.2m\] by \[0.08m\] by\[0.05m\].
Calculate the value of force:-
\[F = {\text{ }}M{\text{ }} \times {\text{ }}g\]
\[ \Rightarrow F = 5 \times 10\]
\[\therefore F = {\text{ }}50\]
So the value of force is 50 Newton. Since, the force is constant we can let \[F{\text{ }} = {\text{ }}K\], and we have
$P = \dfrac{K}{A}$
Therefore, pressure is inversely proportional to area i.e., bigger area equals less pressure. Smaller area equals bigger pressure.
So, we would want to apply the force on the face of the block with the smallest dimensions if we want to find the greatest pressure, i.e. that is \[0.05m{\text{ }} \times {\text{ }}0.08m\] and \[A = {\text{ }}0.004{m^2}\]
So, the greatest pressure will be $P = \dfrac{{50}}{{0.004}} = {\text{ }}12500pa$
If we want to apply the least possible pressure, we must apply force on the biggest dimensions, and that is \[0.2m{\text{ }} \times {\text{ }}0.08m\] and \[A = {\text{ }}0.016{m^2}\]
So, the least pressure will be \[P{\text{ }} = \;\dfrac{{50}}{{0.016}} = {\text{ }}3125pa\]

Note:- (i) The Pascal is the SI unit of pressure used to quantify internal pressure, stress, young's modulus and ultimate tensile strength.
(ii) g is denoted for gravity, the actual value of gravity is \[9.8{\text{ }}m/{s^2}\;\] on Earth.