The neck and bottom of a bottle are 3 cm and 15 cm in radius respectively. If the cork is pressed with a force 12 N in the neck of the bottle, then force exerted on the bottom of the bottle is

30 N

150 N

300 N

600 N

Solution

300 N

Pressure at neck of bottle

P₁ = $\frac{F_{1}}{A_{1}}$

= $\frac{F_{1}}{π r_{1}^{2}}$

Similarly, the pressure at bottom of bottle

P₂ = $\frac{F_{2}}{A_{2}}$

P₂ = $\frac{F_{2}}{π r_{2}^{2}}$

According to Pascal's law, liquids transmits pressure equal in all directions.

$\frac{F_{1}}{{πr}_{1}^{2}} = \frac{F_{2}}{π r_{2}^{2}}$

$\frac{12}{π {(3)}^{2}} = \frac{F_{2}}{π {(15)}^{2}}$

F₂ = $\frac{12 \times 15 \times 15}{3 \times 3}$

F₂ = 300N

Some More Questions From Mechanical Properties of Fluids Chapter

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