06. Flow of Fluid
Mechanical Properties of Fluids

143296 Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density $1.3 \times 10^{3}$. The area of each base is $4.00 \mathrm{~cm}^{2}$, but in one vessel, the liquid height is $0.854 \mathrm{~m}$ and in the other it is $1.560 \mathrm{~m}$. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

1 $0.0635 \mathrm{~J}$
2 $0.635 \mathrm{~J}$
3 $6.35 \mathrm{~J}$
4 $63.5 \mathrm{~J}$
Mechanical Properties of Fluids

143297 A cylindrical container is filled with water upto top. It is a square hole of side $L$ at a depth $y$ from the top. Also there is a circular hole of radius $R=L$ at a depth $2 y$ from the top. Then the ratio of quantities of liquid flowing out through the two holes

1 $\frac{\sqrt{2}}{\pi}$
2 $\frac{1}{\sqrt{2}}$
3 $\frac{1}{2 \pi}$
4 $\frac{1}{\pi \sqrt{2}}$
Mechanical Properties of Fluids

143298 From a water fall, water is falling down at the rate of $500 \mathrm{~kg} / \mathrm{s}$ on the plates of a turbine. If the height of the fall is $50 \mathrm{~m}$, then the power delivered to the turbine is nearly equal to

1 $2.5 \mathrm{~kW}$
2 $250 \mathrm{~kW}$
3 $10 \mathrm{~kW}$
4 $25 \mathrm{~kW}$
Mechanical Properties of Fluids

143299 Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1}=8 \rho_{2}\right)$ and have radii of $1 \mathrm{~mm}$ and 2 $\mathrm{mm}$, respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \rho_{2}$. The ratio of their terminal velocities would be

1 $\frac{29}{72}$
2 $\frac{19}{36}$
3 $\frac{39}{72}$
4 $\frac{79}{36}$
Mechanical Properties of Fluids

143300 A liquid flows along a horizontal pipe $A B$ of uniform cross-section. The difference between the levels of the liquid in tubes $P$ and $Q$ is 10 $\mathrm{cm}$. The diameters of the tubes $P$ and $Q$ are the same. Then $\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$

1 Level in $\mathrm{P}$ is greater then that of $\mathrm{Q}$ and velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
2 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
3 Level in $\mathrm{P}$ is greater than that of $\mathrm{Q}$ and velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
4 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143296 Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density $1.3 \times 10^{3}$. The area of each base is $4.00 \mathrm{~cm}^{2}$, but in one vessel, the liquid height is $0.854 \mathrm{~m}$ and in the other it is $1.560 \mathrm{~m}$. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

1 $0.0635 \mathrm{~J}$
2 $0.635 \mathrm{~J}$
3 $6.35 \mathrm{~J}$
4 $63.5 \mathrm{~J}$
Mechanical Properties of Fluids

143297 A cylindrical container is filled with water upto top. It is a square hole of side $L$ at a depth $y$ from the top. Also there is a circular hole of radius $R=L$ at a depth $2 y$ from the top. Then the ratio of quantities of liquid flowing out through the two holes

1 $\frac{\sqrt{2}}{\pi}$
2 $\frac{1}{\sqrt{2}}$
3 $\frac{1}{2 \pi}$
4 $\frac{1}{\pi \sqrt{2}}$
Mechanical Properties of Fluids

143298 From a water fall, water is falling down at the rate of $500 \mathrm{~kg} / \mathrm{s}$ on the plates of a turbine. If the height of the fall is $50 \mathrm{~m}$, then the power delivered to the turbine is nearly equal to

1 $2.5 \mathrm{~kW}$
2 $250 \mathrm{~kW}$
3 $10 \mathrm{~kW}$
4 $25 \mathrm{~kW}$
Mechanical Properties of Fluids

143299 Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1}=8 \rho_{2}\right)$ and have radii of $1 \mathrm{~mm}$ and 2 $\mathrm{mm}$, respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \rho_{2}$. The ratio of their terminal velocities would be

1 $\frac{29}{72}$
2 $\frac{19}{36}$
3 $\frac{39}{72}$
4 $\frac{79}{36}$
Mechanical Properties of Fluids

143300 A liquid flows along a horizontal pipe $A B$ of uniform cross-section. The difference between the levels of the liquid in tubes $P$ and $Q$ is 10 $\mathrm{cm}$. The diameters of the tubes $P$ and $Q$ are the same. Then $\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$

1 Level in $\mathrm{P}$ is greater then that of $\mathrm{Q}$ and velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
2 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
3 Level in $\mathrm{P}$ is greater than that of $\mathrm{Q}$ and velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
4 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
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Mechanical Properties of Fluids

143296 Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density $1.3 \times 10^{3}$. The area of each base is $4.00 \mathrm{~cm}^{2}$, but in one vessel, the liquid height is $0.854 \mathrm{~m}$ and in the other it is $1.560 \mathrm{~m}$. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

1 $0.0635 \mathrm{~J}$
2 $0.635 \mathrm{~J}$
3 $6.35 \mathrm{~J}$
4 $63.5 \mathrm{~J}$
Mechanical Properties of Fluids

143297 A cylindrical container is filled with water upto top. It is a square hole of side $L$ at a depth $y$ from the top. Also there is a circular hole of radius $R=L$ at a depth $2 y$ from the top. Then the ratio of quantities of liquid flowing out through the two holes

1 $\frac{\sqrt{2}}{\pi}$
2 $\frac{1}{\sqrt{2}}$
3 $\frac{1}{2 \pi}$
4 $\frac{1}{\pi \sqrt{2}}$
Mechanical Properties of Fluids

143298 From a water fall, water is falling down at the rate of $500 \mathrm{~kg} / \mathrm{s}$ on the plates of a turbine. If the height of the fall is $50 \mathrm{~m}$, then the power delivered to the turbine is nearly equal to

1 $2.5 \mathrm{~kW}$
2 $250 \mathrm{~kW}$
3 $10 \mathrm{~kW}$
4 $25 \mathrm{~kW}$
Mechanical Properties of Fluids

143299 Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1}=8 \rho_{2}\right)$ and have radii of $1 \mathrm{~mm}$ and 2 $\mathrm{mm}$, respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \rho_{2}$. The ratio of their terminal velocities would be

1 $\frac{29}{72}$
2 $\frac{19}{36}$
3 $\frac{39}{72}$
4 $\frac{79}{36}$
Mechanical Properties of Fluids

143300 A liquid flows along a horizontal pipe $A B$ of uniform cross-section. The difference between the levels of the liquid in tubes $P$ and $Q$ is 10 $\mathrm{cm}$. The diameters of the tubes $P$ and $Q$ are the same. Then $\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$

1 Level in $\mathrm{P}$ is greater then that of $\mathrm{Q}$ and velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
2 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
3 Level in $\mathrm{P}$ is greater than that of $\mathrm{Q}$ and velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
4 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143296 Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density $1.3 \times 10^{3}$. The area of each base is $4.00 \mathrm{~cm}^{2}$, but in one vessel, the liquid height is $0.854 \mathrm{~m}$ and in the other it is $1.560 \mathrm{~m}$. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

1 $0.0635 \mathrm{~J}$
2 $0.635 \mathrm{~J}$
3 $6.35 \mathrm{~J}$
4 $63.5 \mathrm{~J}$
Mechanical Properties of Fluids

143297 A cylindrical container is filled with water upto top. It is a square hole of side $L$ at a depth $y$ from the top. Also there is a circular hole of radius $R=L$ at a depth $2 y$ from the top. Then the ratio of quantities of liquid flowing out through the two holes

1 $\frac{\sqrt{2}}{\pi}$
2 $\frac{1}{\sqrt{2}}$
3 $\frac{1}{2 \pi}$
4 $\frac{1}{\pi \sqrt{2}}$
Mechanical Properties of Fluids

143298 From a water fall, water is falling down at the rate of $500 \mathrm{~kg} / \mathrm{s}$ on the plates of a turbine. If the height of the fall is $50 \mathrm{~m}$, then the power delivered to the turbine is nearly equal to

1 $2.5 \mathrm{~kW}$
2 $250 \mathrm{~kW}$
3 $10 \mathrm{~kW}$
4 $25 \mathrm{~kW}$
Mechanical Properties of Fluids

143299 Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1}=8 \rho_{2}\right)$ and have radii of $1 \mathrm{~mm}$ and 2 $\mathrm{mm}$, respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \rho_{2}$. The ratio of their terminal velocities would be

1 $\frac{29}{72}$
2 $\frac{19}{36}$
3 $\frac{39}{72}$
4 $\frac{79}{36}$
Mechanical Properties of Fluids

143300 A liquid flows along a horizontal pipe $A B$ of uniform cross-section. The difference between the levels of the liquid in tubes $P$ and $Q$ is 10 $\mathrm{cm}$. The diameters of the tubes $P$ and $Q$ are the same. Then $\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$

1 Level in $\mathrm{P}$ is greater then that of $\mathrm{Q}$ and velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
2 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
3 Level in $\mathrm{P}$ is greater than that of $\mathrm{Q}$ and velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
4 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143296 Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density $1.3 \times 10^{3}$. The area of each base is $4.00 \mathrm{~cm}^{2}$, but in one vessel, the liquid height is $0.854 \mathrm{~m}$ and in the other it is $1.560 \mathrm{~m}$. Find the work done by the gravitational force in equalizing the levels when the two vessels are connected.

1 $0.0635 \mathrm{~J}$
2 $0.635 \mathrm{~J}$
3 $6.35 \mathrm{~J}$
4 $63.5 \mathrm{~J}$
Mechanical Properties of Fluids

143297 A cylindrical container is filled with water upto top. It is a square hole of side $L$ at a depth $y$ from the top. Also there is a circular hole of radius $R=L$ at a depth $2 y$ from the top. Then the ratio of quantities of liquid flowing out through the two holes

1 $\frac{\sqrt{2}}{\pi}$
2 $\frac{1}{\sqrt{2}}$
3 $\frac{1}{2 \pi}$
4 $\frac{1}{\pi \sqrt{2}}$
Mechanical Properties of Fluids

143298 From a water fall, water is falling down at the rate of $500 \mathrm{~kg} / \mathrm{s}$ on the plates of a turbine. If the height of the fall is $50 \mathrm{~m}$, then the power delivered to the turbine is nearly equal to

1 $2.5 \mathrm{~kW}$
2 $250 \mathrm{~kW}$
3 $10 \mathrm{~kW}$
4 $25 \mathrm{~kW}$
Mechanical Properties of Fluids

143299 Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_{1}$ and $\rho_{2}\left(\rho_{1}=8 \rho_{2}\right)$ and have radii of $1 \mathrm{~mm}$ and 2 $\mathrm{mm}$, respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \rho_{2}$. The ratio of their terminal velocities would be

1 $\frac{29}{72}$
2 $\frac{19}{36}$
3 $\frac{39}{72}$
4 $\frac{79}{36}$
Mechanical Properties of Fluids

143300 A liquid flows along a horizontal pipe $A B$ of uniform cross-section. The difference between the levels of the liquid in tubes $P$ and $Q$ is 10 $\mathrm{cm}$. The diameters of the tubes $P$ and $Q$ are the same. Then $\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$

1 Level in $\mathrm{P}$ is greater then that of $\mathrm{Q}$ and velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
2 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $1.4 \mathrm{~m} / \mathrm{s}$
3 Level in $\mathrm{P}$ is greater than that of $\mathrm{Q}$ and velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$
4 Level in $\mathrm{Q}$ is greater than that of $\mathrm{P}$ and Velocity of flow is $0.7 \mathrm{~m} / \mathrm{s}$