Question

A force of 6600 N is exerted on a piston that has an area of 0.010 1" title="m^{2}" alt="m^{2}" align="absmiddle" class="latex-formula">. What area is rewired for a second piston to exert a force of 9900 N? Use $\frac{F_{1} }{A_{1} } = \frac{F_{2} }{A_{2} }$
A. 0.0015 $m^{2}$

B. 66 $m^{2}$

C. 150 $m^{2}$

D. 0.006 $m^{2}$

Answer 1

Answer:

Correct answer is$.015m^2$ which is not any option

Solution

In this question we have given,

force on piston 1,$F_{1}$=6600N

Area of piston 1,$A_{1}$=$.010m^2$

Force on piston 2,$F_{2}$=9900N

we have to find area of piston 2, $A_{2}$=?

According to Pascal's law, the pressure is transmitted with equal intensity to every part of the fluid:

It means,

$p_{1}= p_{2}$

which becomes

$\frac{F_{1} }{A_{1}} =\frac{F_{2} }{A_{2}}$

$A_{2}=\frac{A_{1}\times F_{2}}{F_{1} }$.........(1)

Put values of $A_{1},F_{1} and F_{2}$ in equation 1

$A_{2}=\frac{.010m^2\times 9900N}{6600N}$

$A_{2}=0.015m^2$