Question

an object of 5 kg mass is placed on a cylindrical stand have a circular cross-section the radius of the base of a stand is 4 cm if the same object is placed on cyclinderial stand with radius of the base of a stand is 2 cm then pressure becomes

Answer 1

Case 1 :- Mass of object , m = 5 kg
radius of base of cylindrical stand , r = 4cm = 0.04 m
∵ pressure = Force /base area
Force = weight of body = mg = 5 × 10 = 50 N
base area = πr² = π(0.04)² m²
∴ initial Pressure = 50N/π(0.04)² ------(1)

Case 2 :- radius if base of cylindrical stand , r' = 2cm = 0.02m
∵pressure = force/base area
Force = weight of body = mg = 50N
Base area = πr'² = π (0.02)² m²
∴ final pressure = 50N/π(0.02)² ------(2)

From equations (1) and (2),
Initial pressure /final pressure = {50N/π (0.04)²}/{50N/π(0.02)²}
= 1/4
initial pressure = final pressure/4
Or, final pressure = 4 × initial pressure

Answer 2

Hello Dear.

Here is the answer---


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                       Taking g = 9.8 m/s²

For the First Case,
       Mass of the Object = 5 kg.
 
  Weight of the Object = m × g
                                     = 5 × 9.8
                        Thrust = 49 N

Radius of the Base of the Cylinder(r) = 4 cm.
                                                           = 0.04 m.
Area of the Base of the Cylinder = π r²
                                                    = π × (0.04)²
                                                    = 0.0016 m²

Using the Formula,

 Pressure(P₁)= Thrust/Area
      Pressure = Thrust/π(0.0016)
                     = 49/π(0.0016)

For Second Case,
                     
             Thrust = 49 N 
          [Since the mass of the object is same]
 
Radius of the Cylindrical Stand = 2 cm.
                                                   = 0.02 m.
Area of the Cylindrical Base = π r²
                                              = π (0.004) m²

Thus, Pressure(P₂) = Thrust/Area
                                = Thrust/(0.004)
                                 = 49/π(0.004)

Thus, 
            $\frac{P1}{P2} = \frac{49/ \pi (0.0016)}{49/ \pi(0.004)}$
                   P₁/P₂ = 1/4
              ⇒ P₁ = P₂/4 
              ⇒ P₂ = 4 × P₁

Thus, the Pressure becomes 1/4 of the original pressure in second case.


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Hope it helps.


Have a nice day.