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 $ $ =300\,N $