A force of 6600 N is exerted on a piston that has an area of 0.010 [tex]m^{2}[/tex]. What area is rewired for a second piston to exert a force of 9900 N? Use [tex]\frac{F_{1} }{A_{1} } = \frac{F_{2} }{A_{2} }[/tex]


A. 0.0015 [tex]m^{2}[/tex]

B. 66 [tex]m^{2}[/tex]

C. 150 [tex]m^{2}[/tex]

D. 0.006 [tex]m^{2}[/tex]

Respuesta :

Answer:

Correct answer is[tex].015m^2[/tex] which is not any option

Solution

In this question we have given,

force on piston 1,[tex]F_{1}[/tex]=6600N

Area of piston 1,[tex]A_{1}[/tex]=[tex].010m^2[/tex]

Force on piston 2,[tex]F_{2}[/tex]=9900N

we have to find area of piston 2, [tex]A_{2}[/tex]=?

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

It means,

[tex]p_{1}= p_{2}[/tex]

which becomes

[tex]\frac{F_{1} }{A_{1}} =\frac{F_{2} }{A_{2}}[/tex]

[tex]A_{2}=\frac{A_{1}\times F_{2}}{F_{1} }[/tex].........(1)

Put values of [tex]A_{1},F_{1} and F_{2}[/tex] in equation 1

[tex]A_{2}=\frac{.010m^2\times 9900N}{6600N}[/tex]

[tex]A_{2}=0.015m^2[/tex]