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Archimedes' principle - class-XI

Description: archimedes' principle
Number of Questions: 38
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Tags: properties of matter physics fluid pressure
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A rectangular block is $10\ cm \times 10\ cm \times 15\ cm$ in size is floating in water with $10\ cm$ side vertical. If it floats with $15\ cm$ side vertical, then the level of water will

  1. $Rise$

  2. $Fall$

  3. $Remain\ same$

  4. $Change\ according\ to\ density\ of\ block$


Correct Option: C

A boat having some iron pieces is floating in a pond. If iron pieces are thrown in the liquid then level of liquid 

  1. Increases

  2. Decreases

  3. May increase or decrease

  4. Neither increases nor decreases


Correct Option: B

A coil of wire of cross-section$0.50$ $m m ^ { 2 }4$ weighs $75g$ in air and $65g$ in water. The length of the coil in cm is

  1. $\frac { 10 ^ { 2 } } { 50 }$

  2. $\frac { 10 ^ { 2 } } { 0.50 }$

  3. $\frac { 10 ^ { 5 } } { 50 }$

  4. $\frac { 10 ^ { 5 } } { 0.0050 }$


Correct Option: C

A hollow metal container floats in water, because it displaces _____ weight of water than/as its own weight.

  1. more

  2. less

  3. same

  4. can't say


Correct Option: C
Explanation:

FALSE
If hollow metal container  displaces more weight of water than its own weight it will sink.
Because, we know that by Archimedes principle, the weight of water displaced should be equal to the weight of the part submerged in water. If the weight is greater than the weight of the object, it will sink.

A piece of ice floats in a liquid denser than water.The liquid fills the vessel upto the edge. If ice melts completely then:

  1. water level remains unchanged

  2. water level decreases

  3. water overflows

  4. data is insufficient


Correct Option: C
Explanation:

Density of ice is less than that of water. If it melts it becomes water. But still, the density of liquid is greater than water therefore, water remains on top and thus it floats and then overflows.

State whether the given statement is True or False :

When submerged, a $3N$ block appears to weigh only $1N$. The missing weight is equal to the weight of the water.

  1. True

  2. False


Correct Option: A
Explanation:

Objects weigh more in air than in water. When submerged, the 3 N block appears to weigh only 1 N. The missing weight is equal to the weight of the water displaced. The 2 N weight is equal to the buoyant force.
That is, Loss in weight of body = Weight of water (liquid) displaced by the body = Buoyant force or upthrust exerted by water (any liquid) on the body.

A body of density 5.34  $ \displaystyle g/cm^{3} $ when immersed in water (density 1.0$ \displaystyle g/cm^{3} $ ) will 

  1. float

  2. sink

  3. rise

  4. none of these


Correct Option: B
Explanation:

 

Any solid floats on water if its density is less than the density of water(i.e. 1).So, it will sink.

A piece of iron [density 7.6$ \displaystyle gcm^{-3} $] sinks in mercury [density 13.6 $ \displaystyle gcm^{-3} $]. State whether true or false.

  1. True

  2. False


Correct Option: B
Explanation:

Since condition for sinking of a body of density $\sigma $ in a liquid of density S is 

                  $\sigma >S.$
& Since iron of density 7.69/cc is less lighter than density of mercury (density 13.6g/cc). Hence iron will float on mercury.

A piece of iron sinks in water but can float in mercury. True or false.

  1. True

  2. False


Correct Option: A
Explanation:

Conditions for sinking of a body of density $\sigma $ in a liquid of density S is 

           $\sigma \quad >\quad S$
hence iron sink in water & float in mercury as iron is lighter than mercury.

When an object is placed in a liquid whose density is lower than the object, the object will float. True or false.

  1. True

  2. False


Correct Option: B
Explanation:

a body of higher density would sink in a liquid of lower density 

so the given object would sink in this case
hence option (B) would be correct.

A body having density less than 1 $ \displaystyle gcm^{-3} $ floats in water. True or false

  1. True

  2. False


Correct Option: A
Explanation:

Conditions of a body of density $\sigma $ to float in liquid of density S is 

         $\sigma \quad \le \quad S$
hence a body of density 1gm/cc will float in water.

why does an iron rod sink in water?

  1. The density of rod is more than that of water

  2. The volume of water is more than the weight of the object

  3. Both A and B

  4. None of the above


Correct Option: A
Explanation:

The buoyant force depends on the density of liquid. When the density of the object is more than the density of the liquid, it sinks because the gravitational force acting on the object is more than the buoyant force of water.

State whether True or False.

Objects that sink will always displace their volume. 

  1. True

  2. False


Correct Option: A
Explanation:

Objects that sink will always displace the same volume of water as that of body which gives the net buoyant force applied on the body.

A body of mass 400 g has a volume of 300 cm$^3$. Will body sink in water or not? [Density of water = 1000 kg/m$^3$]

  1. Sink

  2. Float

  3. Sink partly

  4. Float partly


Correct Option: A
Explanation:
Given :     Density of water     $\rho _w = 1000$ $kg/m^3  = 1$ $g/(cm)^3$
Density of body        $\rho _s = \dfrac{M}{V} = \dfrac{400}{300} = 1.33$  $g/(cm)^2$
$\implies$     $\rho _s >\rho _w$
Thus the body will sink in water.

A slid floats in a liquid in a partially dipped position.

  1. The solid exerts a force equal to its weight on the liquid

  2. The weight of the displaced liquid equals the weight of the solid

  3. The liquid exerts a force of buoyancy on the solid which is equal to the weight of the solid

  4. The weight of the dipped part of the solid is equal to the weight of the displaced liquid


Correct Option: A,B,C
Explanation:

The force that solid exerts on liquid is its weight. Hence option A is correct.
Since the solid is stationary, the weight of solid is equal to the force exerted on it by liquid.
According to Archimedes' Principle, the buoyant force acting upwards on the solid is equal to the weight of the liquid displaced. Hence option B and C are correct.

A balloon lifting in air follows:

  1. Law of gravitation

  2. Archimedes principle

  3. Laws of motion

  4. all of the above


Correct Option: D
Explanation:

In a lifting balloon, force of gravitation acts downwards as on all other materials present on the earth, given by $mg$.

Also Archimedes' principle acts on the balloon to provide a buoyant force $V\rho g$ upwards, and greater in magnitude than the gravitational force downwards. (Where $\rho$ is the density of air)
Hence Newton's law of motion provides the acceleration of the balloon upwards, given by: $ma=V\rho g-mg$

When a body is wholly or partly immersed in a liquid it experiences. 

  1. An up-thrust or down-thrust depending on the density of the liquid

  2. An up-thrust

  3. A down-thrust

  4. None of the above


Correct Option: B
Explanation:

Whenever a body is wholly or partially immersed in a liquid it experience an upthrust or buoyant force.

The principle on which Hare's apparatus works on is.

  1. Bernoulli's principle

  2. Archimedes principle

  3. Newton's law

  4. Kepler's law


Correct Option: B
Explanation:

Hare`s apparatus is used  to compare the densities of two liquids and is base on Archimedes principle .

so option (B) is correct

The upward thrust exerted on the body by the liquid acts vertically upwards through the center of gravity of the displaced liquid.

  1. True

  2. False


Correct Option: A
Explanation:

when a body is immersed in a fluid an downward force mg acts on it and to balance this force an upward force kown by the name buoyant force is exerted by the fluid .

so given statement is true , hence option ( A) is correct

A body is floating in a given liquid with half of its volume above the surface of the given liquid. If the body is slightly pushed into the liquid, then the body,

  1. sinks in the liquid and settles at the bottom.

  2. come back to its position after some time.

  3. keeps oscillating in vertical direction.

  4. it jumps into the air and falls on the liquid.


Correct Option: B
Explanation:

Before pushing body was in the position of equilibrium so if we disturbs the eqm than with the passage of time it would come back to its eqm position .

so option (B) is correct

Apparent loss of weight of a body when immersed in a liquid can be explained on the basis of 

  1. molecular theory.

  2. electron theory.

  3. Archimedes' principle.

  4. Bernoulli's principle.


Correct Option: C
Explanation:

Archimedes principle states that  loss in weight of a partially or fully immersed body in a fluid is equal to the weight of the fluid displaced .

so , option (C) is correct

A ball floats on the surface of water in a container exposed to the atmosphere. Will the ball remain immersed at its former depth or will it sink or rise if the container is covered and the air is removed:

  1. The ball sinks

  2. The ball rises

  3. The ball remains immersed at its former depth

  4. It oscillates


Correct Option: A

A piece of ice is floating on water in a container. What will happen to the surface of the water when whole ice piece melts

  1. Will go up

  2. Will not change

  3. Will go down

  4. Noe of these


Correct Option: B
Explanation:
The water level eill not change. As the mass of ice before and after melting will remain same. When the ice was floating, the volume of water displaced has the mass equal to that of ice. After melting, that mass of ice has been converted into water. 
Thus there is no net change in level.

In a car lift compressed air exert a force F1 on a small Piston having radius of 5 cm. This pressure is transmitted to second piston of radius 15 cm. If the mass of the car to be lifted is 1350 kg. What is F1?

  1. $14.7\times 10^3 N$

  2. $1.47\times  10^2 N$

  3. $2.47\times  10^3 N$

  4. $24.7\times 10^2 N$


Correct Option: C

A wooden block is taken to the bottom of a lake of water and then released . it rise up with a 

  1. Constant acceleration

  2. Decreasing acceleration

  3. Constant velocity

  4. Decreasing velocity


Correct Option: A

Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by

  1. Bernoulli

  2. Archimedes

  3. Boyle

  4. Pascal


Correct Option: A

A cube of wood supporting $200 \mathrm { gm }$ mass just floats in water in fully submerged state. When the mass is removed cube rises by $2 \mathrm { cm }$ above water level. Find the size of cube? (take $\rho _ { \text { water } } = 1000 \mathrm { kg } / \mathrm { m } ^ { 3 } )$

  1. $10 \mathrm { cm }$

  2. $15 \mathrm { cm }$

  3. $20 \mathrm { cm }$

  4. $30 \mathrm { cm }$


Correct Option: C

A piece of ice is floating in a beaker containing thick sugar solution of water. As the ice melts, the total level of the liquid:

  1. increases

  2. decreases

  3. remains unchanged

  4. insufficient data


Correct Option: A
Explanation:

Let $\rho $=density of sugar solution $> \rho _{w}$
m=mass of ice.
In floating condition weight=upthrust
$\therefore $   $mg=V _{I}\rho g$
or $\displaystyle V _{I}=\frac{m}{\rho }$          (i)
When ice melts, m mass of ice becomes m mass of water. Volume of this water formed.
$\displaystyle V _{F}=\frac{m}{\rho _{w}}$          (ii)
Since $\rho _{w}< \rho $, $V _{F}> V _{I}$. Hence level will increase.

A boat full of scrap iron is floating on water in a lake. If all the iron is dropped into the water, the level of water will:

  1. go up

  2. fall down

  3. remain the same

  4. Can not be decided.


Correct Option: B
Explanation:
According to Archimedes' principle, any body completely or partially submerged in a fluid at rest is acted upon by an upward, or buoyant force,the magnitude of which is equal to the weight of the fluid displaced by the body
As boat filled with scrap iron is floating on lake, buoyant force acting on boat is more than its weight.
                                              $F _b > W _b + W _{fe}$
since,                                    $W _b<W _b +W _{fe}$
therefore,level of water will fall down across the boat.

If a piece of wood just floats in water. What happens to it in ethanol?

  1. It floats higher

  2. It stays as before

  3. It sinks

  4. First sinks and then rises


Correct Option: C
Explanation:

At room temperature and standard pressure, the first family of alcohol (methanol, ETHANOL and iso-propyl) all have densities of about 0.79g/cc compare to water at the same conditions with a density of 1.0g/cc.

Since the density of ethanol is less than the density of water so, when a piece of wood which is just floating in water is placed in ethanol, sinks.

Which of the following instrument is used to measure the volume of a solid by water displacement ?

  1. Thermometer

  2. Graduated cylinder

  3. Buret

  4. Salt bridge

  5. Conductivity tester


Correct Option: B
Explanation:

Graduated cylinder  is used to measure the volume of a solid by water displacement. The volume of water displaced will be equal to the volume of the solid.

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

  1. It will rise

  2. It will fall

  3. It will remain unchanged

  4. First it will rise and then fall


Correct Option: B

A dog is sitting in a boat which is floating in a pond. If the dog drinks some water from the pond then:

  1. the level of water in the pond decreases

  2. the level of water in the pond increases

  3. the level of water in the pond first increases, then decreases

  4. the level of water in the pond remains unchanged


Correct Option: D
Explanation:

There Will be no change in the water level of the pond, as the water which was drawn from the pond went to the man's body, thereby increasing his weight. So the decrease in level of water will be compensated by volume displaced by increase in weight of the man.

Therefore option $D$ is correct.

A vessel completely filled with water is weighed. This vessel will weigh ________ after a wooden block is gently moved into the water until it stays in equilibrium while any displaced water is removed.

  1. More

  2. Same

  3. Less

  4. None of the above


Correct Option: B
Explanation:

False because the liquid displaced has the same weight as the wooden block has The weight of the displaced liquid from the vessel is same as the weight of the wooden block.
Hence,  the weight will remain the same.

A sphere is floating in water its $\dfrac{1}3rd$ part is outside the water and when the sphere is floating in unknown liquid, it's $\dfrac {3}{4}th$ part is outside the liquid than the density of the liquid is

  1. $\dfrac{4}9\ gm/cc$

  2. $\dfrac{9}4\ gm/cc$

  3. $\dfrac{8}3\ gm/cc$

  4. $\dfrac{3}8\ gm/cc$


Correct Option: C
Explanation:

volume of liquid inside the liquid1=2/3rd of total volume

volume of liquid inside the liquid2 = 1/4th of total volume

density of liquid= (2/3)/(1/4) = 8/3 g/cc

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 raise and then fall


Correct Option: A
Explanation:

Since the weight remains constant & so does buoyant force on a floating body. Hence there will be no change in level of water.

Choose the correct statement from the following:

  1. A body will sink in a liquid if its weight is equal to or greater than the weight of the liquid displaced by it

  2. A body will float in a liquid if its weight is equal to or less then the weight of liquid displaced by it

  3. When a body floats in a liquid, the portion of the body above the surface of the liquid is independent of the density of the body relative to that of the liquid

  4. In still air, a hydrogen filled balloon rises up to certain height and then stops rising.


Correct Option: B,D
Explanation:
According to Archimedes
${ F } _{ b }=$weight of liquid displaced by object
The object floats if ${ F } _{ b }\ge mg$
Weight of liquid displace$\ge $ weight of object
When a body floats the portion immersed or above liquid is dependent on body's density.
The balloon rises till ${ F } _{ b }> mg$. Then stops, since ${ F } _{ b }$ decreases as air gets thin.

Why an iron nail floats on mercury but it sinks in water?

  1. Density of iron is more than that of mercury, but less than that of water.

  2. Density of iron is less than that of mercury, but more than that of water.

  3. Density of iron is less than that of mercury and water

  4. Density of iron is more than that of mercury, water.


Correct Option: B
Explanation:

This is because density of mercury is more than that of water.
An object floats on a liquid, if its density is lower than that of the liquid. 
The density of iron nail is more than that of the water but less than that of mercury.

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