Question

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

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

Answer 1

The correct option is C $300N$

By Pascal's law, the pressure applied to a static and ideal fluid at any point is transmitted equally and undiminished in all directions. In this case the pressure due to the force applied at the neck is transmitted to the bottom.

Thus, pressure at the bottom $=$ pressure at the neck

Therefore, force at the bottom $=$ pressure at the bottom times area of the bottom surface $=$ pressure at the neck times area of the bottom surface.

$F_{bottom}=P_{bottom}\times A_{bottom}=P_{neck}\times A_{neck}=\frac{F_{neck}\times A_{bottom}}{A_{neck}}$

Since, radius of bottom surface is 5 times the radius of the neck that implies area of the bottom surface must be 25 times that of the neck.

Therefore, force applied at the bottom is 25 times the force applied at the neck.

$\Rightarrow F_{Bottom}=25\times 12=300N$