Question

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

• A. $30N$
• B. $150 \, N$
• C. $300 \, N$
• D. $600 \, N$

Answer 1

Answer: (C)

Pressure at neck of bottle
$p_{1}=\frac{F_{1}}{A_{1}}=\frac{F_{1}}{\pi \, r_{1}^{2}}$
Similarly, pressure at bottom of bottle
$p_{2}=\frac{F_{2}}{A_{2}}=\frac{F_{2}}{\pi \, r_{2}^{2}}$
According to Pascal's law, liquids transmits pressure equal in all directions.
$\therefore $ $\frac{F_{2}}{A_{2}}=\frac{F_{2}}{\left(\pi \, r\right)_{2}^{2}} \, or \, F_{2}=F_{1}\times \left(\frac{r_{2}}{r_{1}}\right)^{2}$
$=12\times \left(\frac{15}{3}\right)^{2}=12\times 25=300 \, N$