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Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Fluids2 Marks
Question
Two syringes of different cross$-$sections $($without needles$)$ filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are $1.0\ cm$ and $3.0\ cm$ respectively.
  1. Find the force exerted on the larger piston when a force of $10N$ is applied to the smaller piston.
  2. If the smaller piston is pushed in through $6.0\ cm$, how much does the larger piston move out?
✓

Answer

Here, $d_1 = 1.0\ cm, d_2 = 3.0\ cm$, Force on smaller piston $F_1 = 10N$.
  1. According to Pascal's law of transmission of pressure $\text{P}=\frac{\text{F}_1}{\text{A}_1}=\frac{\text{F}_2}{\text{A}_2}.$
$\therefore\frac{\text{F}_2}{\text{F}_1}=\frac{\text{A}_2}{\text{A}_1}$
$=\frac{\text{r}^2_2}{\text{r}^2_1}=\Big(\frac{\text{d}_2}{\text{d}_1}\Big)^2$
$=\Big(\frac{3.00\text{cm}}{1.0\text{cm}}\big)^2=9$
$\Rightarrow\text{F}_2=\text{F}_1\times9$
$=10\times9$
$=90\text{N}.$
  1. Water is considered to be completely incompressible. Therefore, volume covered by the movement of smaller piston inwards is exactly equal to volume moved outwards due to movement of larger piston, distance through which smaller piston is pushed $L_1 = 6.0\ cm$. Let larger piston is pushed by a distance $L_2$ then,
$\text{V}=\text{L}_1\text{A}_1=\text{L}_2\text{A}_2$
$\therefore\text{L}_2=\text{L}_1\Big(\frac{\text{A}_1}{\text{A}_2}\Big)=\text{L}_2\Big(\frac{\text{d}_1}{\text{d}_2}\Big)^2$
$=6.0\text{cm}\times\Big(\frac{1.0\text{cm}}{3.0\text{cm}}\Big)^2$
$=\frac69\text{cm}$
$=0.67\text{cm}$

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