Question

In hydraulic pressure a force of 200n is applied to a master piston of area 25cm². If the pressure is designed to produce 5000n. Determine the radius of the slave piston

Answer 1

Given

• Input force = 200 N
• Output force = 5000 N
• Area of the master piston = 25 cm²

To Find

• Radius of the slave piston

Solution

☯ F₁/F₂ = A₁/A₂

• The above formula is also called as the Pascal's law

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✭ According to the Question :

➞ F₁/F₂ = A₁/A₂

➞ 200/5000 = 25/x

➞ A₂ = (25 × 5000)/200

➞ A₂ = 625 cm²

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So then the Radius of the slave piston would be,

• πr² = 625
• r² = 625/3.14
• r = √199
• r = 14.1 cm

∴ The radius of the slave piston is 14.1 cm

Answer 2

Given : Applied Force ( $\bf F_1$ ) is 200 N , Produced Force is ($\bf F_2$) & Area of Master Piston is ($\bf A_1$) 25 cm² .

To Find : Radius of slave Piston .

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⠀⠀⠀⠀⠀⠀⠀Firstly , we need To Find Area of Slave Piston .

❒ Let's Consider Area of Slave Piston be x .

⠀⠀⠀⠀⠀⠀⠀By PASCAL'S LAW :

$\qquad \dag \qquad \boxed {\: \pink {\sf \qquad \dfrac{ F_1 }{F_2 } \:\: = \:\:\dfrac{ A_1}{A_2} \qquad }}$

⠀⠀⠀⠀⠀⠀⠀Here , $\sf F_1$ is the Applied Force, $\sf F_2$ is the Produced Force $\sf A_1$ is the Area of Master Piston & $\sf A_2$ is the Area of Slave Piston .

$\qquad \dashrightarrow \:\sf \dfrac{ F_1 }{F_2 } = \dfrac{ A_1}{A_2}$

$\qquad \dashrightarrow \:\sf \dfrac{ 200 }{5000 } = \dfrac{ 25 }{x}$

$\qquad \dashrightarrow \:\sf 200x = 25 ( 5000 )$

$\qquad \dashrightarrow \:\sf 200x = 125000$

$\qquad \dashrightarrow \:\sf x = \dfrac{ 125000 }{200}$

$\qquad \dashrightarrow \:\sf x = 625$

$\qquad \dashrightarrow \pmb{\underline{\purple{\:x = 625\:cm^2 }} }\:\;\bigstar$

⠀⠀⠀⠀⠀Here , x signifies Area of Slave Piston which is 625 cm²

⠀⠀⠀⠀⠀Now , Radius of Slave Piston :

$\qquad \dashrightarrow \:\sf Area_{(Slave \:Piston \:)}= \pi \:r^2$

$\qquad \dashrightarrow \:\sf 625 = \pi \:r^2$

$\qquad \dashrightarrow \:\sf 625 = 3.14 \times \:r^2$

$\qquad \dashrightarrow \:\sf \dfrac{625}{3.14} = \:r^2$

$\qquad \dashrightarrow \:\sf 199 = \:r^2$

$\qquad \dashrightarrow \:\sf \sqrt {199 } = \:r$

$\qquad \dashrightarrow \:\sf 14.1 = \:r$

$\qquad \dashrightarrow \pmb{\underline{\purple{\:r = 14.1\:cm }} }\:\;\bigstar$

⠀⠀⠀⠀⠀$\therefore {\underline{ \sf \:Hence,\:Radius \:of\:Slave \:Piston \:is\:\bf 14.1 \: cm\: }}$