Question

The neck and bottom of a bottle are 3 cm and 15 cm in radius respectively. If ?e 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. 30 N
• 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 Pascals law, liquids transmitspressure equal in all directions. $\therefore$ $\frac{F_1}{\pi r_1^2}=\frac{F_2}{\pi r_2^2}$ or $F_2=F_1\times {\left(\frac{r_2}{r_1}\right)}^2$ $=12\times {\left(\frac{15}{3}\right)}^2$ $=12\times 25$ $=300N$