Physics
(a) The diameter of neck and bottom of a bottle are 2 cm and 10 cm respectively. The bottle is completely filled with oil. If the cork in the neck is pressed in with a force of 1.2 kgf, what force is exerted on the bottom of the bottle ?
(b) Name the law/principle you have used to find the force in part (a)
Fluids Pressure
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Answer
(a) As we know,
Pressure (P) =
and by the principle of hydraulic machine
Pressure on neck = pressure on bottom of bottle
Hence,
{1}}{A{1}} = \dfrac{F{2}}{A{2}} \\[0.5em]
Given,
Diameter of neck (d1) = 2 cm
Hence, A1 = 𝜋 = 𝜋
Diameter of bottom of bottle (d2) = 10 cm
Hence, A2 = 𝜋 = 25 𝜋
Force applied on the cork in the neck (F1) = 1.2 kgf
Substituting the values in the formula above we get,
{2}}{25\pi} \\[0.5em] F{2} = 1.2 \times 25 \\[0.5em] F_{2} = 30 \text{ kgf} \\[0.5em]
Hence, force exerted at the bottom of the neck = 30 kgf.
(b) The Pascal's law is applied to solve the part (a) which states that the pressure exerted anywhere in a confined liquid is transmitted equally and undiminished in all directions throughout the liquid.
Hence,
{1}}{A{1}} = \dfrac{F{2}}{A{2}} \\[0.5em]
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