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Application of Pascal's Law

In the given ...

Question

In the given system, if we change $A_{1}$ into $5 A_{1}$ and $F_{1}$ into $F_{1} / 2$ , then the pressure at B piston changes from $P$ to $P_{0}$ . Calculate the ratio of $P$ and $P_{0}$ .

1 : 5

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5 : 1

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10 : 1

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1 : 10

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Solution

The correct option is C $10 : 1$
According to the Pascal's law, pressure at both pistons are equal as they are on the same level.
$P_{1} = P_{2}$

Case 1:
$⟹ \frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}} = P$

Case 2:
$\frac{F_{1} / 2}{5 A_{1}} = P_{0}$
$P_{0} = \frac{F_{1}}{10 A_{1}}$

The ratio of $P$ and $P_{0}$ is:
$\frac{P}{P_{0}} = \frac{F_{1} / A_{1}}{F_{1} / 10 A_{1}} = 10 : 1$

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Similar questions

A_{1}

2 A_{1}

A_{2}

\frac{A_{2}}{2}

F_{1}

10 F_{1}

P

P_{0}

P

P_{0}

20^{\circ} C

P_{1} = 1.01 \times 10^{5} Pa

P_{2} = 1.165 \times 10^{5} Pa

10

P_{0}

P = \frac{P_{0}}{1 + (V_{0} / V)^{2}}

P_{0}

V_{0}

V = V_{0}

V = 2 V_{0}

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