Floating

Q.

Two solids A and B float in water. It is observed that A floats with half of its volume immersed and B floats with 2/3 of its volume immersed. Compare the densities of A and B

1. 4 : 3

2. 2 : 3

3. 3 : 4

4. 1 : 3

Q.

A cube of wood supporting a mass of 200 g just floats in water. When the mass is removed, the cube rises by 2 cm. What is the size of the cube?

1. 6 cm

2. 8 cm

3. 10 cm

4. 12 cm

Q.

The spring balance A reads 2kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure in this situation:

1. The balance A will read more than 2 kg

2. The balance B will read more than 5 kg

3. The balance A will read less than 2 kg and B will read more than 5 kg

4. The balance A and B will read 2 kg and 5 kg respectively

Q. An ice cube contains a large air bubble. The cube is floating on the surface of water contained on a trough. What will happen to the water level, when the cube melts?

1. It will remain unchanged

2. It will fall

3. Increases with temperature

4. Decreases with temperature

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. 4.8 kg

2. 5.2 kg

3. 5 kg

4. 4.2 kg

Q.

When a solid sphere moves through a liquid, the liquid opposes the motion with a force F. The

magnitude of F depends on the coefficient of viscosity $\eta$ of the liquid, the radius r of the sphere and the speed v of the sphere.

Assuming that F is proportional to different powers of these quantities, guess a formula for F using the

method of dimensions. Use F = -$\frac{\eta A(v_2-v_1)}{x_2-x_1}$

1. 

2. 

3. 

4. None of these

Q.

A boat floating in a tank of water is carrying passengers. If the passengers drink some of the water surrounding the boat in the tank , how will it affect the water level of the tank?

1. It will go down

2. It will rise

3. It will remain unchanged

4. It will depend on atmospheric pressure

Q.

A large cylindrical tank has a hole of area A at its bottom. Water is poured in the tank by a tube of equal cross-sectional area A ejecting water at the speed v.

1. No water can be stored in the tank

2. The water level in the tank will keep on rising

3. The water level will rise to a height g and then stop

4. The water level will oscillate

Q. Two cylinders of same cross-section and length $L$ but made of two different materials of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with a length $\frac{L}{2}$ above the surface of the liquid. If $d_1<d_2$ then

1. $d_1<\frac{3}{4}d$
2. $\frac{d}{2}>d_1$
3. $\frac{d}{4}>d_1$
4. $d<d_1$

Q.

A block of mass 10 kg is attached to the end of two light spring balances combination as shown in figure. What mass will each spring reads? (assume springs are collaborated so that its reading provides the mass)

1. None of these

2. 20kg

3. 10 kg

4. 5 kg

Q. A right circular cone of density $\rho ,$ floats just immersed with its vertex downwards, in a vessel containing two liquids of densities ${\sigma }_1$ and ${\sigma }_2$ respectively. The plane of separation of the two liquids cuts off from the axis of the cone at a fraction $z$ (taken from vertex) of its length. Find $z$.

1. $h{\left(\frac{\rho +{\sigma }_2}{{\sigma }_1+{\sigma }_2}\right)}^{1/3}$
2. $h{\left(\frac{\rho -{\sigma }_2}{{\sigma }_1-{\sigma }_2}\right)}^{1/3}$
3. $h{\left(\frac{\rho -{\sigma }_2}{{\sigma }_1+{\sigma }_2}\right)}^{1/2}$
4. $h\left(\frac{\rho -{\sigma }_2}{{\sigma }_1-{\sigma }_2}\right)$

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 equal volumes

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

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

4. A and B have same weight in air

Q. When body is completely or partially immersed in a fluid and it is in the unstable equilibrium, what is the relation between forces acting on it ?

1. Buoyancy force = Weight of body
2. Buoyancy force > Weight of body
3. Buoyancy force < Weight of body
4. None of the mentioned

Q. The fraction of a floating object of volume $V_{0}anddensity{d}_0$ above the surface of a liquid of density d will be

1. 
2. 
3. 
4. 

Q.

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

1. 0.94 m

2. 0.97 m

3. 0.98 m

4. 0.99 m

Q. A hollow wooden cylinder of height $h$, inner radius $R$ and outer radius $2R$ is placed in a cylindrical container of radius $3R$. When water is poured into the container, the minimum height $H$ of the container for which cylinder can float inside freely is

1. $\frac{h{\rho }_{water}}{{\rho }_{water}+{\rho }_{wood}}$
2. $\frac{h{\rho }_{wood}}{{\rho }_{water}}$
3. $h$
4. $\frac{h^2}{R}$

Q. A concrete sphere of radius $R$ has a spherical cavity of radius $r$ which is packed with sawdust. The specific gravities of concrete and sawdust are respectively $2.4$ and $0.3$. For this sphere to float with its entire volume submerged under water, ratio of mass of concrete to the mass of sawdust will be

1. $8$
2. $4$
3. $3$
4. $1$

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 ice berg of density 900 Kg/$m^3$ is floating in water of density 1000 Kg/$m^3$. The percentage of volume of ice-cube outside the water is

1. 20%
2. 35%
3. 10%
4. 25%

Q. A metallic sphere floats in an immiscible mixture of water and a liquid such that its $\frac{4}{5}\text{th}$ volume is in water and $\frac{1}{5}\text{th}$ volume is in the liquid. Then, density of the metal is

1. $3.5\times {10}^3{\text{kg/m}}^3$
2. $1.5\times {10}^3{\text{kg/m}}^3$
3. $4\times {10}^3{\text{kg/m}}^3$
4. $2\times {10}^3{\text{kg/m}}^3$

Q. When a cube of wood floats in water, $60\%$ of its volume is submerged. When the same cube floats in an unknown fluid, $85\%$ of its volume is submerged. Then:

1. Density of wood is $500{\text{kg/m}}^3$
2. Density of wood is $600{\text{kg/m}}^3$
3. Density of the unknown fluid is $800{\text{kg/m}}^3$
4. Density of the unkonwn fluid is $706{\text{kg/m}}^3$

Q.

A block of mass 10 kg is attached to the end of two light spring balances combination as shown in figure. What mass will each spring reads? (assume springs are collaborated so that its reading provides the mass)

1. 5 kg

2. 20 kg

3. none of these

4. 10 kg

Q. A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of $1.5\times {10}^{-2}N$ (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film ?

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 (in $\text{m}$)
[Answer upto two decimal places]

Q.

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

1. 0.98 m

2. 0.94 m

3. 0.97 m

4. 0.99 m

Q. A right circular cone of density $\rho ,$ floats just immersed with its vertex downwards, in a vessel containing two liquids of densities ${\sigma }_1$ and ${\sigma }_2$ respectively. The plane of separation of the two liquids cuts off from the axis of the cone at a fraction $z$ (taken from vertex) of its length. Find $z$.

1. $h{\left(\frac{\rho +{\sigma }_2}{{\sigma }_1+{\sigma }_2}\right)}^{1/3}$
2. $h{\left(\frac{\rho -{\sigma }_2}{{\sigma }_1-{\sigma }_2}\right)}^{1/3}$
3. $h{\left(\frac{\rho -{\sigma }_2}{{\sigma }_1+{\sigma }_2}\right)}^{1/2}$
4. $h\left(\frac{\rho -{\sigma }_2}{{\sigma }_1-{\sigma }_2}\right)$

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. 

2. 

3. 

4. 

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 fisherman hooks an old log of wood of weight 12N and volume 1000 $c{m}^3$. He pulls the log half way out of water. The tension in the string at this instant is

1. 12 N

2. 8 N

3. 8 N

4. 7 N

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. $\text{Only when}{\rho }_b=P_L=1000{\text{kg/m}}^3$