07. Law of Floating Bodies
Mechanical Properties of Fluids

143304 A body $P$ floats in water with half its volume immersed. Another body $Q$ floats in a liquid of density $3 / 4$ th of the density of water with twothird of the volume immersed. The ratio of density of $P$ to that of $Q$ is

1 $1: 2$
2 $1: 1$
3 $2: 1$
4 $2: 3$
5 $3: 4$
Mechanical Properties of Fluids

143307 Water flows through a hose pipe whose internal diameter is $4 \mathrm{~cm}$ at a speed of $1 \mathrm{~ms}^{-1}$. If water has to emerge at a speed of $4 \mathrm{~ms}^{-1}$, then the diameter of the nozzle should be

1 $1 \mathrm{~cm}$
2 $2 \mathrm{~cm}$
3 $4 \mathrm{~cm}$
4 $0.5 \mathrm{~cm}$
Mechanical Properties of Fluids

143308 A $0.5 \mathrm{~kg}$ block of brass (density $=8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ ) is suspended from a string. What is the tension in the string if the block is completely immersed in water? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$

1 $5 \mathrm{~N}$
2 $\frac{0.5}{8 \times 10^{3}}$
3 $\frac{5}{8} \mathrm{~N}$
4 $\frac{35}{8} \mathrm{~N}$
Mechanical Properties of Fluids

143309 A liquid drop of density $\rho$ is floating half immersed in a liquid of surface tension $S$ and density $\frac{\rho}{2}$. If the surface tension $S$ of the liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is:

1 $\sqrt{\frac{20}{\rho}}$
2 $\sqrt{\frac{80}{\rho}}$
3 $\sqrt{\frac{60}{\rho}}$
4 $\sqrt{\frac{40}{\rho}}$
Mechanical Properties of Fluids

143310 A body of density $\rho^{\prime}$ is dropped from rest at a height $h$ into a lake of density $\rho$ where $\rho>\rho^{\prime}$ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:

1 $\frac{\mathrm{h}}{\rho-\rho^{\prime}}$
2 $\frac{\mathrm{h} \rho^{\prime}}{\rho}$
3 $\frac{h \rho^{\prime}}{\rho-\rho^{\prime}}$
4 $\frac{\mathrm{h} \rho}{\rho-\rho^{\prime}}$
Mechanical Properties of Fluids

143304 A body $P$ floats in water with half its volume immersed. Another body $Q$ floats in a liquid of density $3 / 4$ th of the density of water with twothird of the volume immersed. The ratio of density of $P$ to that of $Q$ is

1 $1: 2$
2 $1: 1$
3 $2: 1$
4 $2: 3$
5 $3: 4$
Mechanical Properties of Fluids

143307 Water flows through a hose pipe whose internal diameter is $4 \mathrm{~cm}$ at a speed of $1 \mathrm{~ms}^{-1}$. If water has to emerge at a speed of $4 \mathrm{~ms}^{-1}$, then the diameter of the nozzle should be

1 $1 \mathrm{~cm}$
2 $2 \mathrm{~cm}$
3 $4 \mathrm{~cm}$
4 $0.5 \mathrm{~cm}$
Mechanical Properties of Fluids

143308 A $0.5 \mathrm{~kg}$ block of brass (density $=8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ ) is suspended from a string. What is the tension in the string if the block is completely immersed in water? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$

1 $5 \mathrm{~N}$
2 $\frac{0.5}{8 \times 10^{3}}$
3 $\frac{5}{8} \mathrm{~N}$
4 $\frac{35}{8} \mathrm{~N}$
Mechanical Properties of Fluids

143309 A liquid drop of density $\rho$ is floating half immersed in a liquid of surface tension $S$ and density $\frac{\rho}{2}$. If the surface tension $S$ of the liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is:

1 $\sqrt{\frac{20}{\rho}}$
2 $\sqrt{\frac{80}{\rho}}$
3 $\sqrt{\frac{60}{\rho}}$
4 $\sqrt{\frac{40}{\rho}}$
Mechanical Properties of Fluids

143310 A body of density $\rho^{\prime}$ is dropped from rest at a height $h$ into a lake of density $\rho$ where $\rho>\rho^{\prime}$ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:

1 $\frac{\mathrm{h}}{\rho-\rho^{\prime}}$
2 $\frac{\mathrm{h} \rho^{\prime}}{\rho}$
3 $\frac{h \rho^{\prime}}{\rho-\rho^{\prime}}$
4 $\frac{\mathrm{h} \rho}{\rho-\rho^{\prime}}$
Mechanical Properties of Fluids

143304 A body $P$ floats in water with half its volume immersed. Another body $Q$ floats in a liquid of density $3 / 4$ th of the density of water with twothird of the volume immersed. The ratio of density of $P$ to that of $Q$ is

1 $1: 2$
2 $1: 1$
3 $2: 1$
4 $2: 3$
5 $3: 4$
Mechanical Properties of Fluids

143307 Water flows through a hose pipe whose internal diameter is $4 \mathrm{~cm}$ at a speed of $1 \mathrm{~ms}^{-1}$. If water has to emerge at a speed of $4 \mathrm{~ms}^{-1}$, then the diameter of the nozzle should be

1 $1 \mathrm{~cm}$
2 $2 \mathrm{~cm}$
3 $4 \mathrm{~cm}$
4 $0.5 \mathrm{~cm}$
Mechanical Properties of Fluids

143308 A $0.5 \mathrm{~kg}$ block of brass (density $=8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ ) is suspended from a string. What is the tension in the string if the block is completely immersed in water? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$

1 $5 \mathrm{~N}$
2 $\frac{0.5}{8 \times 10^{3}}$
3 $\frac{5}{8} \mathrm{~N}$
4 $\frac{35}{8} \mathrm{~N}$
Mechanical Properties of Fluids

143309 A liquid drop of density $\rho$ is floating half immersed in a liquid of surface tension $S$ and density $\frac{\rho}{2}$. If the surface tension $S$ of the liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is:

1 $\sqrt{\frac{20}{\rho}}$
2 $\sqrt{\frac{80}{\rho}}$
3 $\sqrt{\frac{60}{\rho}}$
4 $\sqrt{\frac{40}{\rho}}$
Mechanical Properties of Fluids

143310 A body of density $\rho^{\prime}$ is dropped from rest at a height $h$ into a lake of density $\rho$ where $\rho>\rho^{\prime}$ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:

1 $\frac{\mathrm{h}}{\rho-\rho^{\prime}}$
2 $\frac{\mathrm{h} \rho^{\prime}}{\rho}$
3 $\frac{h \rho^{\prime}}{\rho-\rho^{\prime}}$
4 $\frac{\mathrm{h} \rho}{\rho-\rho^{\prime}}$
Mechanical Properties of Fluids

143304 A body $P$ floats in water with half its volume immersed. Another body $Q$ floats in a liquid of density $3 / 4$ th of the density of water with twothird of the volume immersed. The ratio of density of $P$ to that of $Q$ is

1 $1: 2$
2 $1: 1$
3 $2: 1$
4 $2: 3$
5 $3: 4$
Mechanical Properties of Fluids

143307 Water flows through a hose pipe whose internal diameter is $4 \mathrm{~cm}$ at a speed of $1 \mathrm{~ms}^{-1}$. If water has to emerge at a speed of $4 \mathrm{~ms}^{-1}$, then the diameter of the nozzle should be

1 $1 \mathrm{~cm}$
2 $2 \mathrm{~cm}$
3 $4 \mathrm{~cm}$
4 $0.5 \mathrm{~cm}$
Mechanical Properties of Fluids

143308 A $0.5 \mathrm{~kg}$ block of brass (density $=8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ ) is suspended from a string. What is the tension in the string if the block is completely immersed in water? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$

1 $5 \mathrm{~N}$
2 $\frac{0.5}{8 \times 10^{3}}$
3 $\frac{5}{8} \mathrm{~N}$
4 $\frac{35}{8} \mathrm{~N}$
Mechanical Properties of Fluids

143309 A liquid drop of density $\rho$ is floating half immersed in a liquid of surface tension $S$ and density $\frac{\rho}{2}$. If the surface tension $S$ of the liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is:

1 $\sqrt{\frac{20}{\rho}}$
2 $\sqrt{\frac{80}{\rho}}$
3 $\sqrt{\frac{60}{\rho}}$
4 $\sqrt{\frac{40}{\rho}}$
Mechanical Properties of Fluids

143310 A body of density $\rho^{\prime}$ is dropped from rest at a height $h$ into a lake of density $\rho$ where $\rho>\rho^{\prime}$ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:

1 $\frac{\mathrm{h}}{\rho-\rho^{\prime}}$
2 $\frac{\mathrm{h} \rho^{\prime}}{\rho}$
3 $\frac{h \rho^{\prime}}{\rho-\rho^{\prime}}$
4 $\frac{\mathrm{h} \rho}{\rho-\rho^{\prime}}$
Mechanical Properties of Fluids

143304 A body $P$ floats in water with half its volume immersed. Another body $Q$ floats in a liquid of density $3 / 4$ th of the density of water with twothird of the volume immersed. The ratio of density of $P$ to that of $Q$ is

1 $1: 2$
2 $1: 1$
3 $2: 1$
4 $2: 3$
5 $3: 4$
Mechanical Properties of Fluids

143307 Water flows through a hose pipe whose internal diameter is $4 \mathrm{~cm}$ at a speed of $1 \mathrm{~ms}^{-1}$. If water has to emerge at a speed of $4 \mathrm{~ms}^{-1}$, then the diameter of the nozzle should be

1 $1 \mathrm{~cm}$
2 $2 \mathrm{~cm}$
3 $4 \mathrm{~cm}$
4 $0.5 \mathrm{~cm}$
Mechanical Properties of Fluids

143308 A $0.5 \mathrm{~kg}$ block of brass (density $=8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ ) is suspended from a string. What is the tension in the string if the block is completely immersed in water? $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$

1 $5 \mathrm{~N}$
2 $\frac{0.5}{8 \times 10^{3}}$
3 $\frac{5}{8} \mathrm{~N}$
4 $\frac{35}{8} \mathrm{~N}$
Mechanical Properties of Fluids

143309 A liquid drop of density $\rho$ is floating half immersed in a liquid of surface tension $S$ and density $\frac{\rho}{2}$. If the surface tension $S$ of the liquid is numerically equal to 10 times of acceleration due to gravity, then the diameter of the drop is:

1 $\sqrt{\frac{20}{\rho}}$
2 $\sqrt{\frac{80}{\rho}}$
3 $\sqrt{\frac{60}{\rho}}$
4 $\sqrt{\frac{40}{\rho}}$
Mechanical Properties of Fluids

143310 A body of density $\rho^{\prime}$ is dropped from rest at a height $h$ into a lake of density $\rho$ where $\rho>\rho^{\prime}$ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:

1 $\frac{\mathrm{h}}{\rho-\rho^{\prime}}$
2 $\frac{\mathrm{h} \rho^{\prime}}{\rho}$
3 $\frac{h \rho^{\prime}}{\rho-\rho^{\prime}}$
4 $\frac{\mathrm{h} \rho}{\rho-\rho^{\prime}}$