07. Law of Floating Bodies
Mechanical Properties of Fluids

143335 A body floats in water with $40 \%$ of its volume outside water. When the same body floats in oil, $60 \%$ of its volume remains outside oil. The relative density of the oil is

1 0.9
2 1.2
3 1.5
4 1.8
Mechanical Properties of Fluids

143336 A body of density $1.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ is dropped from rest from a height $1 \mathrm{~m}$ into a liquid of density $2.4 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on the surface is

1 $0.1 \mathrm{~m}$
2 $1 \mathrm{~m}$
3 $0.01 \mathrm{~m}$
4 $2 \mathrm{~m}$
Mechanical Properties of Fluids

143337 A cylindrical block floats vertically in a liquid of density $\rho_{1}$ kept in a container such that the fraction of volume of the cylinder inside the liquid is $x_{1}$. Then some amount of another immiscible liquid of density $\rho_{2}\left(\rho_{2} \lt \rho_{1}\right)$ is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with $x_{2}$ fraction of volume of the cylinder inside the liquid of density $\rho_{1}$. The ratio $\rho_{1} / \rho_{2}$ will be

1 $\frac{1-x_{2}}{x_{1}-x_{2}}$
2 $\frac{1-x_{1}}{x_{1}+x_{2}}$
3 $\frac{x_{1}-x_{2}}{x_{1}+x_{2}}$
4 $\frac{x_{2}}{x_{1}}-1$
Mechanical Properties of Fluids

143340 A wooden block of density $0.5 \mathrm{~g} / \mathrm{cc}$ is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density $1 \mathrm{~g} / \mathrm{cc}$. If the tension of the string is $20 \mathrm{~N}$, then the mass of the block is:

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

143335 A body floats in water with $40 \%$ of its volume outside water. When the same body floats in oil, $60 \%$ of its volume remains outside oil. The relative density of the oil is

1 0.9
2 1.2
3 1.5
4 1.8
Mechanical Properties of Fluids

143336 A body of density $1.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ is dropped from rest from a height $1 \mathrm{~m}$ into a liquid of density $2.4 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on the surface is

1 $0.1 \mathrm{~m}$
2 $1 \mathrm{~m}$
3 $0.01 \mathrm{~m}$
4 $2 \mathrm{~m}$
Mechanical Properties of Fluids

143337 A cylindrical block floats vertically in a liquid of density $\rho_{1}$ kept in a container such that the fraction of volume of the cylinder inside the liquid is $x_{1}$. Then some amount of another immiscible liquid of density $\rho_{2}\left(\rho_{2} \lt \rho_{1}\right)$ is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with $x_{2}$ fraction of volume of the cylinder inside the liquid of density $\rho_{1}$. The ratio $\rho_{1} / \rho_{2}$ will be

1 $\frac{1-x_{2}}{x_{1}-x_{2}}$
2 $\frac{1-x_{1}}{x_{1}+x_{2}}$
3 $\frac{x_{1}-x_{2}}{x_{1}+x_{2}}$
4 $\frac{x_{2}}{x_{1}}-1$
Mechanical Properties of Fluids

143340 A wooden block of density $0.5 \mathrm{~g} / \mathrm{cc}$ is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density $1 \mathrm{~g} / \mathrm{cc}$. If the tension of the string is $20 \mathrm{~N}$, then the mass of the block is:

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

143335 A body floats in water with $40 \%$ of its volume outside water. When the same body floats in oil, $60 \%$ of its volume remains outside oil. The relative density of the oil is

1 0.9
2 1.2
3 1.5
4 1.8
Mechanical Properties of Fluids

143336 A body of density $1.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ is dropped from rest from a height $1 \mathrm{~m}$ into a liquid of density $2.4 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on the surface is

1 $0.1 \mathrm{~m}$
2 $1 \mathrm{~m}$
3 $0.01 \mathrm{~m}$
4 $2 \mathrm{~m}$
Mechanical Properties of Fluids

143337 A cylindrical block floats vertically in a liquid of density $\rho_{1}$ kept in a container such that the fraction of volume of the cylinder inside the liquid is $x_{1}$. Then some amount of another immiscible liquid of density $\rho_{2}\left(\rho_{2} \lt \rho_{1}\right)$ is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with $x_{2}$ fraction of volume of the cylinder inside the liquid of density $\rho_{1}$. The ratio $\rho_{1} / \rho_{2}$ will be

1 $\frac{1-x_{2}}{x_{1}-x_{2}}$
2 $\frac{1-x_{1}}{x_{1}+x_{2}}$
3 $\frac{x_{1}-x_{2}}{x_{1}+x_{2}}$
4 $\frac{x_{2}}{x_{1}}-1$
Mechanical Properties of Fluids

143340 A wooden block of density $0.5 \mathrm{~g} / \mathrm{cc}$ is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density $1 \mathrm{~g} / \mathrm{cc}$. If the tension of the string is $20 \mathrm{~N}$, then the mass of the block is:

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

143335 A body floats in water with $40 \%$ of its volume outside water. When the same body floats in oil, $60 \%$ of its volume remains outside oil. The relative density of the oil is

1 0.9
2 1.2
3 1.5
4 1.8
Mechanical Properties of Fluids

143336 A body of density $1.2 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ is dropped from rest from a height $1 \mathrm{~m}$ into a liquid of density $2.4 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on the surface is

1 $0.1 \mathrm{~m}$
2 $1 \mathrm{~m}$
3 $0.01 \mathrm{~m}$
4 $2 \mathrm{~m}$
Mechanical Properties of Fluids

143337 A cylindrical block floats vertically in a liquid of density $\rho_{1}$ kept in a container such that the fraction of volume of the cylinder inside the liquid is $x_{1}$. Then some amount of another immiscible liquid of density $\rho_{2}\left(\rho_{2} \lt \rho_{1}\right)$ is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with $x_{2}$ fraction of volume of the cylinder inside the liquid of density $\rho_{1}$. The ratio $\rho_{1} / \rho_{2}$ will be

1 $\frac{1-x_{2}}{x_{1}-x_{2}}$
2 $\frac{1-x_{1}}{x_{1}+x_{2}}$
3 $\frac{x_{1}-x_{2}}{x_{1}+x_{2}}$
4 $\frac{x_{2}}{x_{1}}-1$
Mechanical Properties of Fluids

143340 A wooden block of density $0.5 \mathrm{~g} / \mathrm{cc}$ is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density $1 \mathrm{~g} / \mathrm{cc}$. If the tension of the string is $20 \mathrm{~N}$, then the mass of the block is:

1 $1 \mathrm{~kg}$
2 $2 \mathrm{~kg}$
3 $3 \mathrm{~kg}$
4 $0.5 \mathrm{~kg}$