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Question: Calculate the greatest and the least pressure exerted by a metal block of size \[20cm{\text{ }} \tim...

Calculate the greatest and the least pressure exerted by a metal block of size 20cm ×8cm×5cm20cm{\text{ }} \times 8cm \times 5cm and having mass 5kg5kg. Take g=10/s2g = 10/{s^2}.

  1. 12500pa ; 3125pa12500pa{\text{ }};{\text{ }}3125pa
  2. 11500pa ; 3125pa  11500pa{\text{ }};{\text{ }}3125pa\;
    3)13500pa ; 5125pa13500pa{\text{ }};{\text{ }}5125pa
  3. 12500pa; 5125pa12500pa;{\text{ }}5125pa
Explanation

Solution

Hint:- Find the value of force by given value ofg=10/s2g = 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=FAP = \dfrac{F}{A}
Where F is the force in Newton, P is the pressure in Pascal and A is the area in m2{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 0.2m0.2m by 0.08m0.08m by0.05m0.05m.
Calculate the value of force:-
F= M × gF = {\text{ }}M{\text{ }} \times {\text{ }}g
⇒F=5×10\Rightarrow F = 5 \times 10
∴F= 50\therefore F = {\text{ }}50
So the value of force is 50 Newton. Since, the force is constant we can let F = KF{\text{ }} = {\text{ }}K, and we have
P=KAP = \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 × 0.08m0.05m{\text{ }} \times {\text{ }}0.08m and A= 0.004m2A = {\text{ }}0.004{m^2}
So, the greatest pressure will be P=500.004= 12500paP = \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 × 0.08m0.2m{\text{ }} \times {\text{ }}0.08m and A= 0.016m2A = {\text{ }}0.016{m^2}
So, the least pressure will be P =  500.016= 3125paP{\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 m/s2  9.8{\text{ }}m/{s^2}\; on Earth.