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Course of The First World War - Eastern War Front

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 $P_{0}$ .

A

10 : 1

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B

5 : 1

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C

1 : 10

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D

1 : 5

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Solution

The correct option is A $10 : 1$
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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