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WB JEE Medical WB JEE Medical Solved Paper-2006

  • question_answer
    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

    Correct Answer: C

    Solution :

                     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                            \[{{F}_{2}}={{F}_{1}}\times {{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\]                                 \[=12\times {{\left( \frac{15}{3} \right)}^{2}}\] \[=12\times 25\] \[=300\,N\]


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