02. Capillary and Angle of Contact
Mechanical Properties of Fluids

143002 When a capillary is dipped vertically in water, rise of water in capillary is ' $h$ '. The angle of contact is zero. Now the tube is depressed so that its length above the water surface is $\frac{h}{2}$. The new apparent angle of contact is $\left(\cos 0^{\circ}=\right.$ 1).

1 $\sin ^{-1}(0.5)$
2 $\cos ^{-1}(0.5)$
3 $\cos ^{-1}(0.7)$
4 $\sin ^{-1}(0.7)$
Mechanical Properties of Fluids

143006 If a capillary tube is immersed vertically in water, rise of water in capillary is ' $h_{1}$ '. When the whole arrangement is taken to a depth ' $d$ ' in a mine, the water level rises to ' $h_{2}$ '. The ratio $\frac{h_{1}}{h_{2}}$ is $(R=$ radius of earth)

1 $\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)$
2 $\left(1+\frac{d}{R}\right)$
3 $\left(1+\frac{\mathrm{d}^{2}}{\mathrm{R}^{2}}\right)$
4 $\left(1-\frac{\mathrm{d}^{2}}{\mathrm{R}^{2}}\right)$
Mechanical Properties of Fluids

143007 Two capillary tubes of different diameters are dipped in water. The rise of water is

1 more in the tube of larger diameter
2 zero in both the tubes
3 same in both the tubes
4 more in the tube of smaller diameter
Mechanical Properties of Fluids

143008 In a capillary tube of radius ' $R$ ', a straight thin metal wire of radius ' $r$ ' $(R>r)$ is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is $T=$ surface tension of water, $\rho=$ density of water, $\mathbf{g}$ = gravitational acceleration

1 $\frac{\mathrm{T}}{(\mathrm{R}+\mathrm{r}) \rho g}$
2 $\frac{\mathrm{R} \rho g}{2 \mathrm{~T}}$
3 $\frac{2 \mathrm{~T}}{(\mathrm{R}-\mathrm{r}) \rho g}$
4 $\frac{(R-r) \rho g}{T}$
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Mechanical Properties of Fluids

143002 When a capillary is dipped vertically in water, rise of water in capillary is ' $h$ '. The angle of contact is zero. Now the tube is depressed so that its length above the water surface is $\frac{h}{2}$. The new apparent angle of contact is $\left(\cos 0^{\circ}=\right.$ 1).

1 $\sin ^{-1}(0.5)$
2 $\cos ^{-1}(0.5)$
3 $\cos ^{-1}(0.7)$
4 $\sin ^{-1}(0.7)$
Mechanical Properties of Fluids

143006 If a capillary tube is immersed vertically in water, rise of water in capillary is ' $h_{1}$ '. When the whole arrangement is taken to a depth ' $d$ ' in a mine, the water level rises to ' $h_{2}$ '. The ratio $\frac{h_{1}}{h_{2}}$ is $(R=$ radius of earth)

1 $\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)$
2 $\left(1+\frac{d}{R}\right)$
3 $\left(1+\frac{\mathrm{d}^{2}}{\mathrm{R}^{2}}\right)$
4 $\left(1-\frac{\mathrm{d}^{2}}{\mathrm{R}^{2}}\right)$
Mechanical Properties of Fluids

143007 Two capillary tubes of different diameters are dipped in water. The rise of water is

1 more in the tube of larger diameter
2 zero in both the tubes
3 same in both the tubes
4 more in the tube of smaller diameter
Mechanical Properties of Fluids

143008 In a capillary tube of radius ' $R$ ', a straight thin metal wire of radius ' $r$ ' $(R>r)$ is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is $T=$ surface tension of water, $\rho=$ density of water, $\mathbf{g}$ = gravitational acceleration

1 $\frac{\mathrm{T}}{(\mathrm{R}+\mathrm{r}) \rho g}$
2 $\frac{\mathrm{R} \rho g}{2 \mathrm{~T}}$
3 $\frac{2 \mathrm{~T}}{(\mathrm{R}-\mathrm{r}) \rho g}$
4 $\frac{(R-r) \rho g}{T}$
Mechanical Properties of Fluids

143002 When a capillary is dipped vertically in water, rise of water in capillary is ' $h$ '. The angle of contact is zero. Now the tube is depressed so that its length above the water surface is $\frac{h}{2}$. The new apparent angle of contact is $\left(\cos 0^{\circ}=\right.$ 1).

1 $\sin ^{-1}(0.5)$
2 $\cos ^{-1}(0.5)$
3 $\cos ^{-1}(0.7)$
4 $\sin ^{-1}(0.7)$
Mechanical Properties of Fluids

143006 If a capillary tube is immersed vertically in water, rise of water in capillary is ' $h_{1}$ '. When the whole arrangement is taken to a depth ' $d$ ' in a mine, the water level rises to ' $h_{2}$ '. The ratio $\frac{h_{1}}{h_{2}}$ is $(R=$ radius of earth)

1 $\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)$
2 $\left(1+\frac{d}{R}\right)$
3 $\left(1+\frac{\mathrm{d}^{2}}{\mathrm{R}^{2}}\right)$
4 $\left(1-\frac{\mathrm{d}^{2}}{\mathrm{R}^{2}}\right)$
Mechanical Properties of Fluids

143007 Two capillary tubes of different diameters are dipped in water. The rise of water is

1 more in the tube of larger diameter
2 zero in both the tubes
3 same in both the tubes
4 more in the tube of smaller diameter
Mechanical Properties of Fluids

143008 In a capillary tube of radius ' $R$ ', a straight thin metal wire of radius ' $r$ ' $(R>r)$ is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is $T=$ surface tension of water, $\rho=$ density of water, $\mathbf{g}$ = gravitational acceleration

1 $\frac{\mathrm{T}}{(\mathrm{R}+\mathrm{r}) \rho g}$
2 $\frac{\mathrm{R} \rho g}{2 \mathrm{~T}}$
3 $\frac{2 \mathrm{~T}}{(\mathrm{R}-\mathrm{r}) \rho g}$
4 $\frac{(R-r) \rho g}{T}$
Mechanical Properties of Fluids

143002 When a capillary is dipped vertically in water, rise of water in capillary is ' $h$ '. The angle of contact is zero. Now the tube is depressed so that its length above the water surface is $\frac{h}{2}$. The new apparent angle of contact is $\left(\cos 0^{\circ}=\right.$ 1).

1 $\sin ^{-1}(0.5)$
2 $\cos ^{-1}(0.5)$
3 $\cos ^{-1}(0.7)$
4 $\sin ^{-1}(0.7)$
Mechanical Properties of Fluids

143006 If a capillary tube is immersed vertically in water, rise of water in capillary is ' $h_{1}$ '. When the whole arrangement is taken to a depth ' $d$ ' in a mine, the water level rises to ' $h_{2}$ '. The ratio $\frac{h_{1}}{h_{2}}$ is $(R=$ radius of earth)

1 $\left(1-\frac{\mathrm{d}}{\mathrm{R}}\right)$
2 $\left(1+\frac{d}{R}\right)$
3 $\left(1+\frac{\mathrm{d}^{2}}{\mathrm{R}^{2}}\right)$
4 $\left(1-\frac{\mathrm{d}^{2}}{\mathrm{R}^{2}}\right)$
Mechanical Properties of Fluids

143007 Two capillary tubes of different diameters are dipped in water. The rise of water is

1 more in the tube of larger diameter
2 zero in both the tubes
3 same in both the tubes
4 more in the tube of smaller diameter
Mechanical Properties of Fluids

143008 In a capillary tube of radius ' $R$ ', a straight thin metal wire of radius ' $r$ ' $(R>r)$ is inserted symmetrically and one end of the combination is dipped vertically in water such that the lower end of the combination is at same level. The rise of water in the capillary tube is $T=$ surface tension of water, $\rho=$ density of water, $\mathbf{g}$ = gravitational acceleration

1 $\frac{\mathrm{T}}{(\mathrm{R}+\mathrm{r}) \rho g}$
2 $\frac{\mathrm{R} \rho g}{2 \mathrm{~T}}$
3 $\frac{2 \mathrm{~T}}{(\mathrm{R}-\mathrm{r}) \rho g}$
4 $\frac{(R-r) \rho g}{T}$
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