Floating

Q.

There is some water in the beaker placed on the pan of a spring balance. If we dip our finger in the water without touching the bottom of the beaker, then what is the change in the reading of spring balance?

Q.

A body of weight W, experiences an upthrust R in water. What will be the apparent weight of the body and apparent density of the body when W>R?

Q. A cubical block of ice floating in water has to support a metal piece of mass $0.5\text{kg}$. If specific gravity of ice is $0.9$, then minimum edge length (in $\text{m}$) of the block so that it does not sink in water is

1. ${\left(\frac{1}{200}\right)}^{\frac{1}{3}}\text{m}$
2. ${\left(\frac{1}{150}\right)}^{\frac{1}{3}}\text{m}$
3. ${\left(\frac{1}{100}\right)}^{\frac{1}{3}}\text{m}$
4. ${\left(\frac{1}{250}\right)}^{\frac{1}{3}}\text{m}$

Q. An object of density $\rho$ and volume $V$ floats at the interface of two liquids $1$ and $2$ of densities ${\rho }_1$ and ${\rho }_2$ with volume $V_1$ in liquid $1$ and ${\rho }_2$ in liquid $2$. Then for equilibrium $({\rho }_1<\rho <{\rho }_2)$ value of $\frac{V_2}{V_1}$ is:

1. $\frac{({\rho }_1-{\rho }_2)}{(\rho -{\rho }_1)}$
2. $\frac{({\rho }_2-{\rho }_1)}{(\rho -{\rho }_2)}$
3. $\frac{({\rho }_1-\rho )}{({\rho }_2-\rho )}$
4. $\frac{(\rho -{\rho }_1)}{({\rho }_2-\rho )}$

Q.

A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water?

1. It will remain unchanged

2. It will rise

3. It will fall

4. First it will rise and then fall

Q. A block of wood floats in water with ${\frac{4}{5}}^{\text{th}}$ of its volume submerged but in another liquid, it floats fully submerged. The density of the unknown liquid is (in ${\text{kg/m}}^3$)

1. $750$
2. $800$
3. $1000$
4. $1250$

Q. A vessel contains oil (density $0.8{\text{g/cm}}^2$) over mercury (density $13.6{\text{g/cm}}^3$). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in ${\text{g/cm}}^3$ is

1. $3.3$
2. $6.4$
3. $7.2$
4. $12.8$

Q.

An object weighs $840g$ in air and $680g$ when fully immersed in a liquid. What is the buoyant force on the object due to the liquid?

Q. A body floats in a liquid contained in a beaker. The whole system falls freely under gravity. The upthrust on the body is -

1. Zero
2. Equal to the weight of the liquid displaced
3. Equal to the weight of the body in air.
4. Equal to the weight of the immerssed portion of the body

Q.

A metallic sphere floats in an immiscible mixture of water (density 10${}^3$ kg/m${}^3$) and a liquid (density $8\times {10}^{3}kg/m^3$) such that its ($\frac{2}{3}$) part is in water and ($\frac{1}{3}$) part in the liquid. The density of the metal is

1. $\frac{5000}{3}kg/m^3$

2. $\frac{10000}{3}kg/m^3$

3. $5000kg/m^3$

4. $2000kg/m^3$

Q. A cylindrical block of wood of mass $2\text{kg}$ is floating in water with its axis vertical. It is depressed by a distance $x$ and net force on it is given by $F=kx$. Then, value of $k$ in $\text{N/m}$ is
[Use $\pi =\frac{22}{7}$]

Q. A block of wood floats in water $\left(4/5\right)th$ of its volume submerged. If the same block just floats in a liquid, the density of liquid in ${\text{kg/m}}^3$ is
(Take density of water as $1000{\text{kg/m}}^3$)

1. $900{\text{kg/m}}^3$
2. $400{\text{kg/m}}^3$
3. $1250{\text{kg/m}}^3$
4. $800{\text{kg/m}}^3$

Q. A ball is made of a material of density $\rho$ where, ${\rho }_{\text{oil}}<\rho <{\rho }_{\text{water}}$ with ${\rho }_{\text{oil}}$ and ${\rho }_{\text{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium positions?

1. 
2. 
3. 
4. 

Q. The condition for a body having density ${\rho }_b$ to float completely immersed in the liquid having density ${\rho }_L$ is

1. ${\rho }_b>{\rho }_L$
2. ${\rho }_b<{\rho }_L$
3. ${\rho }_b={\rho }_L$
4. $\text{Only when}{\rho }_b=P_L=1000{\text{kg/m}}^3$

Q. A vessel contains oil (density $0.8{\text{g/cm}}^2$) over mercury (density $13.6{\text{g/cm}}^3$). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in ${\text{g/cm}}^3$ is

1. $3.3$
2. $6.4$
3. $7.2$
4. $12.8$

Q.

A cube of side 20cm is floating on liquid with 5cm of the cube outside the liquid. If the density of liquid is 0.8 gm/c.c then the mass of the cube is

1. 4.2 kg

2. 4.8 kg

3. 5 kg

4. 5.2 kg

Q. A vessel contains oil (density = $0.8{\text{g/cm}}^3)$ over mercury (density = $13.6{\text{g/cm}}^3)$. 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 ${\text{g/cm}}^3$ is

1. $3.3$
2. $6.4$
3. $7.2$
4. $12.8$

Q. A cube floats in water with ${\left(\frac{1}{4}\right)}^{\text{th}}$ part outside the surface of water. If it floats in another liquid of relative density $\frac{4}{3}$ with $x^{th}$ part outside the liquid, then the value of $x$ is

1. $\frac{7}{16}$
2. $\frac{1}{2}$
3. $\frac{8}{15}$
4. $\frac{9}{16}$

Q. A vessel contains oil (density $0.8{\text{g/cm}}^2$) over mercury (density $13.6{\text{g/cm}}^3$). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in ${\text{g/cm}}^3$ is

1. $3.3$
2. $6.4$
3. $7.2$
4. $12.8$

Q. An iceberg is floating in an ocean. What fraction of its volume is above the water? (Given: density of ice$=900{\text{kg/m}}^3$ and density of ocean water $=1030{\text{kg/m}}^3$)

1. $\frac{90}{103}$
2. $\frac{13}{103}$
3. $\frac{10}{103}$
4. $\frac{1}{103}$

Q. A wooden block, with a coin placed on its top, floats in water as shown in fig. The distance $l$ and $h$ are shown there. After some time the coin falls into the water. Then

1. $l$ decreases and $h$ increases
2. $l$ increases and $h$ decreases
3. both $l$ and $h$ increases
4. both $l$ and $h$ decreases

Q. A wooden cube just floats inside water with a $400\text{gm}$ mass placed on it. When the mass is removed, the cube floats with its top surface $4\text{cm}$ above the water level. What is the side of the cube?

1. $6\text{cm}$
2. $8\text{cm}$
3. $10\text{cm}$
4. $12\text{cm}$

Q. A hemispherical bowl just floats without sinking in a liquid of density $1.2\times {10}^3{\text{kg/m}}^3.$ If the outer diameter and the density of the bowl are $1\text{m}$ and $2\times {10}^4{\text{kg/m}}^3$ respectively, then the inner diameter of the bowl will be

1. $0.92\text{m}$
2. $0.94\text{m}$
3. $0.96\text{m}$
4. $0.98\text{m}$

Q. A cubical body floats on mercury with $4\%$ of its volume below the mercury surface. What fraction of the volume of the body will be immersed in the mercury if a layer of water poured on top of the mercury covers the body completely?

[Assume, ${\rho }_m=13.6{\text{g/cm}}^3;{\rho }_w=1{\text{g/cm}}^3$ ]

1. $0.25$
2. $0.35$
3. $0.45$
4. $0.50$

Q. A spherical solid ball of volume $V$ is made of a material of density ${\rho }_1$. It is falling through a liquid of density ${\rho }_1({\rho }_2<{\rho }_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous}=-k{v}^2(k>0)$. The terminal speed of the ball is

1. $\sqrt{\frac{Vg({\rho }_1-{\rho }_2)}{k}}$
2. $\frac{Vg{\rho }_1}{k}$
3. $\sqrt{\frac{Vg{\rho }_1}{k}}$
4. $\frac{Vg({\rho }_1-{\rho }_2)}{k}$

Q. Two cubical blocks identical in dimensions float in water in such a way that the first block floats with half part immersed in water and the second block floats with $3/4\text{th}$ of its volume immersed inside the water. The ratio of density of first block to that of second block is

1. $2:3$
2. $3:4$
3. $1:3$
4. $1:4$

Q. A ball is made of a material of density $\rho$ where, ${\rho }_{\text{oil}}<\rho <{\rho }_{\text{water}}$ with ${\rho }_{\text{oil}}$ and ${\rho }_{\text{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium positions?

1. 
2. 
3. 
4. 

Q. A rectangular block with dimensions $10\text{cm}\times 10\text{cm}\times 15\text{cm}$ is floating in a water container with its $10\text{cm}$ side in vertical position. If it floats with its $15\text{cm}$ side in vertical position, then the level of water in the container will

1. rise
2. fall
3. remain constant
4. changes according to the density of block

Q. A cube of ice floats partly in water and partly in kerosene oil. Specific gravity of kerosene oil and that of ice is $0.8$ and $0.9$ respectively. Ratio of the volume of ice immersed in water to that in kerosene oil is

1. $2:1$
2. $3:1$
3. $1:2$
4. $1:1$

Q.

A and B are two metallic pieces. They are fully immersed in water and then weighed. Now they show same loss of weight. The conclusion therefore is:

1. A and B have same weight in air

2. A and B have equal volumes

3. The densities of the materials of A and B are the same

4. A and B are immersed to the same depth inside water