07. Law of Floating Bodies
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Mechanical Properties of Fluids

143350 A vessel contains oil (density $=0.8 \mathrm{~g} \mathrm{~cm}^{-3}$ ) over mercury (density $=13.6 \mathrm{~g} \mathrm{~cm}^{-3}$ ). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere (in $\mathrm{g} \mathrm{cm}^{-3}$ ) is

1 3.3
2 6.4
3 7.2
4 2.8
Mechanical Properties of Fluids

143351 A body of volume 72 ce floats with $3 / 4^{\text {th }}$ of its volume under water. Find its density, given density of water is $10^{3} \mathrm{~kg} \cdot \mathrm{m}^{-3}$ :

1 $7500 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
2 $750 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
3 $75000 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
4 $750000 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
Mechanical Properties of Fluids

143352 A cube of wood of side $0.25 \mathrm{~m}$ weighing $12.5 \mathrm{~kg}$ floats on water. If the density of water is $\mathbf{1 0 0 0}$ kg. $\mathrm{m}^{-3}$. Find the depth to which the cube is immersed.

1 $5 \mathrm{~m}$
2 $0.5 \mathrm{~m}$
3 $2 \mathrm{~m}$
4 $0.2 \mathrm{~m}$
Mechanical Properties of Fluids

143353 A non-conducting body floats in a liquid at $20^{\circ} \mathrm{C}$ with $\frac{2}{3}$ of its volume immersed in the
liquid. When liquid temperature is increased to $100^{\circ} \mathrm{C}, \frac{3}{4}$ of body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of container of the liquid)

1 $15.6 \times 10^{-40} \mathrm{C}^{-1}$
2 $156 \times 10^{-40} \mathrm{C}^{-1}$
3 $1.56 \times 10^{-4 \circ} \mathrm{C}^{-1}$
4 $0.156 \times 10^{-4_{0}} \mathrm{C}^{-1}$
Mechanical Properties of Fluids

143350 A vessel contains oil (density $=0.8 \mathrm{~g} \mathrm{~cm}^{-3}$ ) over mercury (density $=13.6 \mathrm{~g} \mathrm{~cm}^{-3}$ ). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere (in $\mathrm{g} \mathrm{cm}^{-3}$ ) is

1 3.3
2 6.4
3 7.2
4 2.8
Mechanical Properties of Fluids

143351 A body of volume 72 ce floats with $3 / 4^{\text {th }}$ of its volume under water. Find its density, given density of water is $10^{3} \mathrm{~kg} \cdot \mathrm{m}^{-3}$ :

1 $7500 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
2 $750 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
3 $75000 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
4 $750000 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
Mechanical Properties of Fluids

143352 A cube of wood of side $0.25 \mathrm{~m}$ weighing $12.5 \mathrm{~kg}$ floats on water. If the density of water is $\mathbf{1 0 0 0}$ kg. $\mathrm{m}^{-3}$. Find the depth to which the cube is immersed.

1 $5 \mathrm{~m}$
2 $0.5 \mathrm{~m}$
3 $2 \mathrm{~m}$
4 $0.2 \mathrm{~m}$
Mechanical Properties of Fluids

143353 A non-conducting body floats in a liquid at $20^{\circ} \mathrm{C}$ with $\frac{2}{3}$ of its volume immersed in the
liquid. When liquid temperature is increased to $100^{\circ} \mathrm{C}, \frac{3}{4}$ of body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of container of the liquid)

1 $15.6 \times 10^{-40} \mathrm{C}^{-1}$
2 $156 \times 10^{-40} \mathrm{C}^{-1}$
3 $1.56 \times 10^{-4 \circ} \mathrm{C}^{-1}$
4 $0.156 \times 10^{-4_{0}} \mathrm{C}^{-1}$
Mechanical Properties of Fluids

143350 A vessel contains oil (density $=0.8 \mathrm{~g} \mathrm{~cm}^{-3}$ ) over mercury (density $=13.6 \mathrm{~g} \mathrm{~cm}^{-3}$ ). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere (in $\mathrm{g} \mathrm{cm}^{-3}$ ) is

1 3.3
2 6.4
3 7.2
4 2.8
Mechanical Properties of Fluids

143351 A body of volume 72 ce floats with $3 / 4^{\text {th }}$ of its volume under water. Find its density, given density of water is $10^{3} \mathrm{~kg} \cdot \mathrm{m}^{-3}$ :

1 $7500 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
2 $750 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
3 $75000 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
4 $750000 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
Mechanical Properties of Fluids

143352 A cube of wood of side $0.25 \mathrm{~m}$ weighing $12.5 \mathrm{~kg}$ floats on water. If the density of water is $\mathbf{1 0 0 0}$ kg. $\mathrm{m}^{-3}$. Find the depth to which the cube is immersed.

1 $5 \mathrm{~m}$
2 $0.5 \mathrm{~m}$
3 $2 \mathrm{~m}$
4 $0.2 \mathrm{~m}$
Mechanical Properties of Fluids

143353 A non-conducting body floats in a liquid at $20^{\circ} \mathrm{C}$ with $\frac{2}{3}$ of its volume immersed in the
liquid. When liquid temperature is increased to $100^{\circ} \mathrm{C}, \frac{3}{4}$ of body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of container of the liquid)

1 $15.6 \times 10^{-40} \mathrm{C}^{-1}$
2 $156 \times 10^{-40} \mathrm{C}^{-1}$
3 $1.56 \times 10^{-4 \circ} \mathrm{C}^{-1}$
4 $0.156 \times 10^{-4_{0}} \mathrm{C}^{-1}$
Mechanical Properties of Fluids

143350 A vessel contains oil (density $=0.8 \mathrm{~g} \mathrm{~cm}^{-3}$ ) over mercury (density $=13.6 \mathrm{~g} \mathrm{~cm}^{-3}$ ). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere (in $\mathrm{g} \mathrm{cm}^{-3}$ ) is

1 3.3
2 6.4
3 7.2
4 2.8
Mechanical Properties of Fluids

143351 A body of volume 72 ce floats with $3 / 4^{\text {th }}$ of its volume under water. Find its density, given density of water is $10^{3} \mathrm{~kg} \cdot \mathrm{m}^{-3}$ :

1 $7500 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
2 $750 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
3 $75000 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
4 $750000 \mathrm{~kg} \cdot \mathrm{m}^{-3}$
Mechanical Properties of Fluids

143352 A cube of wood of side $0.25 \mathrm{~m}$ weighing $12.5 \mathrm{~kg}$ floats on water. If the density of water is $\mathbf{1 0 0 0}$ kg. $\mathrm{m}^{-3}$. Find the depth to which the cube is immersed.

1 $5 \mathrm{~m}$
2 $0.5 \mathrm{~m}$
3 $2 \mathrm{~m}$
4 $0.2 \mathrm{~m}$
Mechanical Properties of Fluids

143353 A non-conducting body floats in a liquid at $20^{\circ} \mathrm{C}$ with $\frac{2}{3}$ of its volume immersed in the
liquid. When liquid temperature is increased to $100^{\circ} \mathrm{C}, \frac{3}{4}$ of body's volume is immersed in the liquid. Then the coefficient of real expansion of the liquid is (neglecting the expansion of container of the liquid)

1 $15.6 \times 10^{-40} \mathrm{C}^{-1}$
2 $156 \times 10^{-40} \mathrm{C}^{-1}$
3 $1.56 \times 10^{-4 \circ} \mathrm{C}^{-1}$
4 $0.156 \times 10^{-4_{0}} \mathrm{C}^{-1}$