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.
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Answer 1

Given :-

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

To Find :-

Radius

Solution :-

F1/F2 = A1/A2

200/5000 = 25/A2

25(5000) = 200(A2)

125000 = 200A2

125000/200 = A2

1250/2 = A2

625 = A2

Now

Area = πr²

625 = 3.14 × r²

625/3.14 = r²

199 = r²

√199 = r

14.10 = r

Answer 2

$\pink{ \boxed{\boxed{\begin{array}{cc} \bf \leadsto \: given \\ \\ \rm \to \: Input \: force \:F_1 = 200 \: N \\ \\ \rm \to \: Output \: force \: F_2 = 5000 \: N \\ \\ \rm \to \: Area \: of \: the \: master \: piston \: \: A_1= 25 \: {cm}^{2} \\ \\ \bf \leadsto \: To \: Find \: : \\ \\ \bf \: \to \: Radius \: of \: the \: slave \: piston = r \: \end{array}}}}$

Solution :

$\sf \: we \: know \: that \: \\ \\ \sf \: Pascal's \: law \: : \: \frac{F_1}{F_2} = \frac{A_1}{A_2}$

According to the question,

$\frac{200}{5 000} = \frac{25}{A_2} \\ \\ = > A_2 = \frac{25 \times 5000}{200} \\ \\ = > A_2 = 625 \: {cm}^{2}$

Let,

Radius of the slave piston will be = r

So,

$\sf \: A_2 = \pi {r}^{2} \\ \\ = > 625 = 3.14 \times {r}^{2} \\ \\ = > r = \sqrt{ \frac{625}{3.14} } \\ \\ = > r = 14.1 \: cm$

Finally,

$\sf \: The \: radius \: of \:the \: slave\: piston \: is \: \: r = 14.1 \: cm$