Archimedes' Principle

Q.

A boat having a length of 3m and a breadth of 2m is floating on a lake. The boat sinks by 1cm when a man gets on it. What is the mass of the man?

Q.

A hydrometer stem has a length 0.3 m. If the hydrometer is immersed in water, its floating bulb just sinks. If the same hydrometer is immersed in a liquid of density 0.5 g cm^–3, two third of the stem is immersed. Determine the least specific gravity of a liquid that can be measured using the hydrometer.

1. 0.1

2. 0.2

3. 0.3

4. 0.4

Q. A $700\text{g}$ solid cube having an edge of length $10\text{cm}$ floats in water. How much volume of the cube is outside the water? Density of water $=1{\text{g/cm}}^3.$

1. $700{\text{cm}}^3$
2. $300{\text{cm}}^3$
3. $1000{\text{cm}}^3$
4. $30{\text{cm}}^3$

Q.

How many times lighter or heavier than air is hydrogen?

Q.

A solid floats with 84% of its volume in water. The density of solid is:

1. 0.84 g cm^-3

2. 1.6 g cm^-3

3. 4.8 g cm^-3

4. 8.4 g cm^-3

Q.

A body weighs $W_1$ in a liquid of density $d_1$ and $W_2$ in a liquid of density $d_2$. What is the weight in a liquid of density $d_3$?

1. $W_3$ = $\frac{W_1(d_3-d_1)-W_2(d_3-d_2)}{d_2-d_1}$

2. $W_3$ = $\frac{W_2(d_3-d_1)-W_1(d_3-d_2)}{d_2-d_1}$

3. $W_3$ = $\frac{W_2(d_1-d_2)-W_1(d_3-d_2)}{d_2-d_1}$

4. $W_3$ = $\frac{W_2(d_3-d_1)-W_1(d_3-d_2)}{d_1-d_2}$

Q.

A body weighs $W_1$ in a liquid of density $d_1$ and $W_2$ in a liquid of density $d_2$. What is the weight in a liquid of density $d_3$?

1. $W_3$ = $\frac{W_1(d_3-d_1)-W_2(d_3-d_2)}{d_2-d_1}$

2. $W_3$ = $\frac{W_2(d_3-d_1)-W_1(d_3-d_2)}{d_2-d_1}$

3. $W_3$ = $\frac{W_2(d_1-d_2)-W_1(d_3-d_2)}{d_2-d_1}$

4. $W_3$ = $\frac{W_2(d_3-d_1)-W_1(d_3-d_2)}{d_1-d_2}$

Q. A wooden block, with a coin placed on its top, floats in water as shown in figure. 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. Two non-mixing liquids of densities $\rho$ and $n\rho (n>1)$ are put in a container. The height of each liquid is $h$. A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $pL(p<1)$ in the denser liquid. The density $d$ is equal to:

1. $\left[1+(n+1)p\right]\rho$
2. $\left[2+(n+1)p\right]\rho$
3. $\left[2+(n-1)p\right]\rho$
4. $\left[1+(n-1)p\right]\rho$

Q.

A solid sphere of radius R and density $\rho$ is attached to one end of a massless spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density $3\rho$. The complete arrangement is placed in a liquid of density $2\rho$ and is allowed to reach equilibrium. The correct statement(s) is (are)

1. The net elongation of the spring is $\frac{\left(4\pi R^3\rho g\right)}{3k}$

2. The net elongation of the spring is $\frac{\left(8\pi R^3\rho g\right)}{3k}$

3. The light sphere is partially submerged.

4. The light sphere is completely submerged.

Q. A cube made of material having a density of $900{\text{kg m}}^{-3}$ floats between water of density $1000{\text{kgm}}^{-3}$ and a liquid of density $700{\text{kgm}}^{-3}$ which is immiscible in water. What part of cube is inside the water?

1. 1/2
2. 2/3
3. 3/4
4. 3/7

Q. A small ball of density $\rho$ is immersed in a liquid of density $\sigma (>\rho )$ to a depth h and released. The height above the surface of water up to which the ball will jump is

1. $(\frac{\rho }{\sigma }-1)h$
2. $(\frac{\rho }{\sigma }-1)h$
3. $(\frac{\sigma }{\rho }-1)h$
4. $(\frac{\sigma }{\rho }+1)h$

Q. A $700\text{g}$ solid cube having an edge of length $10\text{cm}$ floats in water. How much volume of the cube is outside the water? Density of water $=1{\text{g/cm}}^3.$

1. $700{\text{cm}}^3$
2. $300{\text{cm}}^3$
3. $1000{\text{cm}}^3$
4. $30{\text{cm}}^3$

Q.

A silver ingot weighing 2.1 kg is held by a string so as to be completely immersed in a liquid of relative density 0.8. The relative density of silver is 10.5. The tension in the string in kg-wt is

1. 1.6

2. 1.94

3. 3.1

4. 5.25

Q.

A concrete sphere of radius R has a 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 mass of sawdust will be

1. 8

2. 4

3. 3

4. Zero

Q. The distance of the centres of moon and earth is $D$. The mass of earth is $81$ times the mass of the moon. At what distance from the centre of the earth, the gravitational force on a particle will be zero.

1. $\frac{4D}{3}$
2. $\frac{2D}{3}$
3. $\frac{9D}{10}$
4. $\frac{D}{2}$

Q. A wire is found to have a length $L$ when it is loaded with a block of mass $M$ and relative density $n$. When the block is immersed in water, the length of the wire reduces by $x$. Then, which of the following is/are correct?

1. Weight of water displaced when the block is immersed in water is $\frac{Mg}{n}$.
2. The apparent loss of weight due to immersion is $Mg(1-\frac{1}{n})$.
3. The original length of wire before it was loaded is $L_1=L-nx$.
4. The original length of the wire before it was loaded is $L_1=L-\frac{x}{n}$.

Q. A wooden block, with a coin placed on its top, floats in water as shown in the figure. The distance $l$ and $h$ are shown. 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 $h$ increase
4. Both $l$ and $h$ decrease

Q. A cylinder of mass $m$ and density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $s$ containing a liquid of density $\sigma (<\rho )$ until it is fully immersed. The increase in pressure at the bottom of the vessel is :

1. $\frac{m\rho g}{\sigma s}$
2. $\frac{mg}{s}$
3. $\frac{m\sigma g}{\rho s}$
4. Zero

Q. A body floats in water with one-third of its volume above the surface of water. If it is placed in oil, it floats with half of its volume above the surface of the oil. The relative density of the oil is

1. $\frac{3}{4}$
2. $\frac{2}{3}$
3. $\frac{4}{3}$
4. $\frac{3}{2}$

Q. An iron casting containing a number of cavities weighs $16000\text{N}$ in air and $12000\text{N}$ in water. Volume of the cavities in the casting is -
[ take density of iron $=8000{\text{kg/m}}^3$ & $g=10{\text{m/s}}^2$]

1. $0.2{\text{m}}^3$
2. $0.3{\text{m}}^3$
3. $0.1{\text{m}}^3$
4. $0.4{\text{m}}^3$

Q.

A boat made of wood is floating in the water with two boys in it. The volume of water displaced is 0.125 m³ . What is the upthrust exerted by water on the boat? How do the two answers compare? Why is this so?

Q. A cylinder of mass $m$ and density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $s$ containing a liquid of density $\sigma (<\rho )$ until it is fully immersed. The increase in pressure at the bottom of the vessel is :

1. $\frac{m\rho g}{\sigma s}$
2. $\frac{mg}{s}$
3. $\frac{m\sigma g}{\rho s}$
4. Zero

Q. A cubical block of wood of edge $3\text{cm}$ floats in water. The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the pot. Find the maximum weight that can be put on the block without wetting it.
(Take density of wood $=800{\text{kg/m}}^3$, spring constant of the spring $=50\text{N/m}$ and $g=10{\text{m/s}}^2$.)

1. $0.35\text{N}$
2. $0.6\text{N}$
3. $0.27\text{N}$
4. $0.78\text{N}$

Q.

A block of steel of size 5 cm $\times$ 5 cm $\times$ 5 cm is weighed in water. If the relative density of steel is 7, its apparent weight is

1. $6\times 5\times 5\times 5$gf

2. $4\times 4\times 4\times 7$gf

3. $5\times 5\times 5\times 7$gf

4. $4\times 4\times 4\times 6$gf

Q. A wire is found to have a length $L$ when it is loaded with a block of mass $M$ and relative density $n$. When the block is immersed in water, the length of the wire reduces by $x$. Then, which of the following is/are correct?

1. Weight of water displaced when the block is immersed in water is $\frac{Mg}{n}$.
2. The apparent loss of weight due to immersion is $Mg(1-\frac{1}{n})$.
3. The original length of wire before it was loaded is $L_1=L-nx$.
4. The original length of the wire before it was loaded is $L_1=L-\frac{x}{n}$.

Q. A piece of wood of mass $6\text{kg}$ is floating in water with its $\frac{1}{3}$rd part inside the water. On this floating piece of wood, what maximum mass can be put such that the whole of the piece of wood gets drowned in the water?

1. $15\text{kg}$
2. $14\text{kg}$
3. $10\text{kg}$
4. $12\text{kg}$

Q.

A body of density $d_1$ is counterpoised by Mg of weights of density $d_2$ in air of density d. Then the true mass of the body is

1. M

2. $M⟮1-\frac{d}{d_2}⟯$

3. $M⟮1-\frac{d}{d_1}⟯$

4. $\frac{M(1-\frac{d}{d_2})}{(1-\frac{d}{d_1})}$

Q. A glass slab ($\mu =1.5)$ of thickness $4\text{cm}$ is pressed against newspaper, the distance by which letter of the paper are seen raised against the paper by someone who is looking at letters along normal to the slab is

1. $\frac{2}{3}\text{cm}$
2. $1\text{cm}$
3. $\frac{4}{3}\text{cm}$
4. $\frac{8}{3}\text{cm}$