02. Capillary and Angle of Contact
Mechanical Properties of Fluids

142990 A capillary tube of length $L$ and radius $r$ is connected with another capillary tube of the same length but half the radius in series. The rate of steady volume flow of water through first capillary tube under a pressure difference of $P$ is $V$. The rate of steady volume flow through the combination will be (the pressure difference across the combination is $P$ )

1 $17 \mathrm{~V}$
2 $\frac{16}{17} \mathrm{~V}$
3 $\frac{\mathrm{V}}{17}$
4 $\frac{17}{16} \mathrm{~V}$
Mechanical Properties of Fluids

142992 Find the height of liquid in capillary tube, if surface tension of liquid $=S$, radius of capillary tube $=r$ and acceleration due to gravity $=g$.

1 $\frac{2 \mathrm{~S} \cos \theta}{\operatorname{\rho rg}}$
2 $\frac{2 \mathrm{~S} .}{\rho \cos \cos \theta}$
3 $\frac{2 \mathrm{~S} \sin \theta}{\operatorname{\rho rg}}$
4 None of these
Mechanical Properties of Fluids

142993 The rate of flow of water in a capillary tube of length $l$ and radius $r$ is $V$. The rate of flow in another capillary tube of length $2 l$ and radius $\mathbf{2} \boldsymbol{r}$ for same pressure difference would be

1 $16 \mathrm{~V}$
2 $9 \mathrm{~V}$
3 $8 \mathrm{~V}$
4 $2 \mathrm{~V}$
Mechanical Properties of Fluids

142994 The lower end of a capillary tube of radius ' $r$ ' is placed vertically in a water of density $\rho$ and surface tension $S$. The rise of water in the capillary tube is upto height $h$, then height $h$, then heat evolved is-

1 $+\frac{\pi^{2} r^{2} h^{2} \rho g}{J}$
2 $+\frac{\pi r^{2} h^{2} \rho g}{2 \mathrm{~J}}$
3 $-\frac{\pi^{2} r^{2} h^{2} \rho g}{2 J}$
4 $-\frac{\pi r^{2} h^{2} \rho g}{J}$
Mechanical Properties of Fluids

142990 A capillary tube of length $L$ and radius $r$ is connected with another capillary tube of the same length but half the radius in series. The rate of steady volume flow of water through first capillary tube under a pressure difference of $P$ is $V$. The rate of steady volume flow through the combination will be (the pressure difference across the combination is $P$ )

1 $17 \mathrm{~V}$
2 $\frac{16}{17} \mathrm{~V}$
3 $\frac{\mathrm{V}}{17}$
4 $\frac{17}{16} \mathrm{~V}$
Mechanical Properties of Fluids

142992 Find the height of liquid in capillary tube, if surface tension of liquid $=S$, radius of capillary tube $=r$ and acceleration due to gravity $=g$.

1 $\frac{2 \mathrm{~S} \cos \theta}{\operatorname{\rho rg}}$
2 $\frac{2 \mathrm{~S} .}{\rho \cos \cos \theta}$
3 $\frac{2 \mathrm{~S} \sin \theta}{\operatorname{\rho rg}}$
4 None of these
Mechanical Properties of Fluids

142993 The rate of flow of water in a capillary tube of length $l$ and radius $r$ is $V$. The rate of flow in another capillary tube of length $2 l$ and radius $\mathbf{2} \boldsymbol{r}$ for same pressure difference would be

1 $16 \mathrm{~V}$
2 $9 \mathrm{~V}$
3 $8 \mathrm{~V}$
4 $2 \mathrm{~V}$
Mechanical Properties of Fluids

142994 The lower end of a capillary tube of radius ' $r$ ' is placed vertically in a water of density $\rho$ and surface tension $S$. The rise of water in the capillary tube is upto height $h$, then height $h$, then heat evolved is-

1 $+\frac{\pi^{2} r^{2} h^{2} \rho g}{J}$
2 $+\frac{\pi r^{2} h^{2} \rho g}{2 \mathrm{~J}}$
3 $-\frac{\pi^{2} r^{2} h^{2} \rho g}{2 J}$
4 $-\frac{\pi r^{2} h^{2} \rho g}{J}$
Mechanical Properties of Fluids

142990 A capillary tube of length $L$ and radius $r$ is connected with another capillary tube of the same length but half the radius in series. The rate of steady volume flow of water through first capillary tube under a pressure difference of $P$ is $V$. The rate of steady volume flow through the combination will be (the pressure difference across the combination is $P$ )

1 $17 \mathrm{~V}$
2 $\frac{16}{17} \mathrm{~V}$
3 $\frac{\mathrm{V}}{17}$
4 $\frac{17}{16} \mathrm{~V}$
Mechanical Properties of Fluids

142992 Find the height of liquid in capillary tube, if surface tension of liquid $=S$, radius of capillary tube $=r$ and acceleration due to gravity $=g$.

1 $\frac{2 \mathrm{~S} \cos \theta}{\operatorname{\rho rg}}$
2 $\frac{2 \mathrm{~S} .}{\rho \cos \cos \theta}$
3 $\frac{2 \mathrm{~S} \sin \theta}{\operatorname{\rho rg}}$
4 None of these
Mechanical Properties of Fluids

142993 The rate of flow of water in a capillary tube of length $l$ and radius $r$ is $V$. The rate of flow in another capillary tube of length $2 l$ and radius $\mathbf{2} \boldsymbol{r}$ for same pressure difference would be

1 $16 \mathrm{~V}$
2 $9 \mathrm{~V}$
3 $8 \mathrm{~V}$
4 $2 \mathrm{~V}$
Mechanical Properties of Fluids

142994 The lower end of a capillary tube of radius ' $r$ ' is placed vertically in a water of density $\rho$ and surface tension $S$. The rise of water in the capillary tube is upto height $h$, then height $h$, then heat evolved is-

1 $+\frac{\pi^{2} r^{2} h^{2} \rho g}{J}$
2 $+\frac{\pi r^{2} h^{2} \rho g}{2 \mathrm{~J}}$
3 $-\frac{\pi^{2} r^{2} h^{2} \rho g}{2 J}$
4 $-\frac{\pi r^{2} h^{2} \rho g}{J}$
Mechanical Properties of Fluids

142990 A capillary tube of length $L$ and radius $r$ is connected with another capillary tube of the same length but half the radius in series. The rate of steady volume flow of water through first capillary tube under a pressure difference of $P$ is $V$. The rate of steady volume flow through the combination will be (the pressure difference across the combination is $P$ )

1 $17 \mathrm{~V}$
2 $\frac{16}{17} \mathrm{~V}$
3 $\frac{\mathrm{V}}{17}$
4 $\frac{17}{16} \mathrm{~V}$
Mechanical Properties of Fluids

142992 Find the height of liquid in capillary tube, if surface tension of liquid $=S$, radius of capillary tube $=r$ and acceleration due to gravity $=g$.

1 $\frac{2 \mathrm{~S} \cos \theta}{\operatorname{\rho rg}}$
2 $\frac{2 \mathrm{~S} .}{\rho \cos \cos \theta}$
3 $\frac{2 \mathrm{~S} \sin \theta}{\operatorname{\rho rg}}$
4 None of these
Mechanical Properties of Fluids

142993 The rate of flow of water in a capillary tube of length $l$ and radius $r$ is $V$. The rate of flow in another capillary tube of length $2 l$ and radius $\mathbf{2} \boldsymbol{r}$ for same pressure difference would be

1 $16 \mathrm{~V}$
2 $9 \mathrm{~V}$
3 $8 \mathrm{~V}$
4 $2 \mathrm{~V}$
Mechanical Properties of Fluids

142994 The lower end of a capillary tube of radius ' $r$ ' is placed vertically in a water of density $\rho$ and surface tension $S$. The rise of water in the capillary tube is upto height $h$, then height $h$, then heat evolved is-

1 $+\frac{\pi^{2} r^{2} h^{2} \rho g}{J}$
2 $+\frac{\pi r^{2} h^{2} \rho g}{2 \mathrm{~J}}$
3 $-\frac{\pi^{2} r^{2} h^{2} \rho g}{2 J}$
4 $-\frac{\pi r^{2} h^{2} \rho g}{J}$