# Gravitation (Floatation) : Practice Questions

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1 Mark Questions

Q.1 Â Define thrust.

Q.2 Â State a condition for an object to float when placed on the surface of water.

Q.3 Â A coin sinks when placed on the surface of water. Give reason.

Q.4 Â State and define SI unit of pressure.

Q.5 Â How is pressure related to the thrust exerted on a surface?

Q.6 Â Why do buildings have wide foundation?

Q.7 Â How does the density of fluid affect the magnitude of buoyancy acting on an object immersed in it?

Q.8 Â State Archimedes principle.

Q.9 Â Give two applications of Archimedes principle.

Q.10 Â Give the SI unit of relative density.

Q.11 Â Relate relative density of a substance to its density.

Q.12 Â Density of a solid is 7.5 ${\rm{g /c}}{{\rm{m}}^3}$ . What is its relative density?

Q.13 Â State the SI unit of buoyancy.

Q.14 Â School bags have broad straps.

Q.15 Â Dams have broad foundation.

Q.16 Â It is easier to cut an apple with sharp edge of knife.

Q.17 Â A mug appears lighter inside water.

Q.18 Â A solid exerts pressure of 20 Pa on a surface of 2 ${m^2}$. Find its weight.

Q.19 Â Relative density of an object is 1.35. Will it float or sink in water?

Q.20 Â Mark the direction of weight of the body and upthrust acting on it, in the following diagram:

Q.21 Â "A coin sinks in water because upthrust acting on it is greater than its weight." Is the statement correct? If not, correct it.

Q.22 Â An object is put one by one in three liquids having different densities. The object floats with 1/9, 2/11 and 3/7 parts of their volumes outside the liquid surface in liquids of densities d1, d2 and d3 respectively.Â  Arrange the densities in ascending order of their magnitude.

Q.23 Â An object weights 10 N in air. When immersed fully in water, it weights 8 N. Find the weight of liquid displaced by the object.

Q.24 Â State the principle of floatation for an object of weight W immersed in a fluid.

Q.25 Â Relate the SI unit of density with its CGS unit.

Q.26 Â A crumpled sheet of paper falls down faster than a plane sheet, Why?

Q.27 Â A body is immersed once in each of the following media:
mustard oil
water
glycerine
petrol
In which ease will there be maximum apparent loss of weight and why?

Q.28 Â Differentiate between force and thrust.

SolutionsÂ

1. Â Force acting perpendicular to a surface is called thrust.

2. Â A body will float if its density is less than that of water.

3. Â The coin sinks as its density is greater than water.

4. Â Pressure is defined as thrust per unit area. The unit of pressure is Pascal. One pascal is the pressure exerted when 1 N force acts as a surface area of 1${m^2}$ .

5. Â Pressure = Thrust/Area

6. Â Buildings have wide foundations to reduce the pressure on ground. Since larger the area, lesser will be the pressure.

7. Â Weight of fluid displaced = $\rho$gV where $\rho$ is the density.Â Hence, buoyant force increases with increasing density of fluid.

8. Â Archimedes Principle: When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

9. Â It is used inÂ  (i) designing ships andÂ  (ii) submarines.

10. Â Relative density has no units.

11. Â Relative density =${{{\rm{Density}}\,{\rm{of}}\,{\rm{substance}}} \over {{\rm{Density}}\,{\rm{of}}\,{\rm{water}}}}$

12. Â Relative density = ${{{\rm{Density}}\,{\rm{of}}\,{\rm{substance}}} \over {{\rm{Density}}\,{\rm{of}}\,{\rm{water}}}}$

$= {{7.5} \over 1} = 7.5$

13. Â Newton.

14. Â Pressure = Force/Area.

Broad straps have greater area and therefore exert lesser pressure.

15. Â Greater the area, less is the pressure exerted. The broad base of dams reduce pressure on the ground.

16. Â Sharp knives have very small area on which the force acts. Hence , pressure is much more and can easily cut an apple.

17. Â The mug appears lighter as the buoyant force acting in the upward direction reduces the effective weight of the mug when placed in water.

18. Â Weight = Pressure X Area

= 20 X 2 = 40 N.

19. Â As relative density is greater thanÂ 1 , the object will sink.

20.Â

${F_B}$ = Buoyant force

W = Weight of object

21. Â The statement is wrong. The correct statement will be " A coin sinks in water because upthrust acting on it is less than its weight".

22. Â ${1 \over 9} = 0.11\,;\,{2 \over {11}} = \,0.18\,;\,{3 \over 7} = 0.43$

There are the volume outside of liquids of densities d1, d2, d3 respectively. This means buoyant face is maximum for d3 and minimum for d2. As buoyant forceÂ  is proportional to density, d1< d2<d3.

23. Â Weight of object in air = 10 N

Weight of object in fluid = 8 N

Therefore, Loss of weight = (10 - 8) N = 2 N

Buoyant force = Loss of weight = 2 N

24. Â Archimedes Principle states when a body is immersed fully or partiallyÂ  in a fluid, it experiences an upward force that is equal to the weight of the fluidÂ  displaced by it.

25. Â 1000 kg/${m^3}$ = $1g\,m/c{m^3}$

26. Â Air resistance on sheet of paper will be more then the crumpled sheet as its surface area is greater. The net force acting on it is nearly zero so it moves down slowly.

27. Â Glycerine has highest density so maximum apparent loss will be seen when body is immersed in glycerine.

28. Â Force can have any direction, but thrust is that force which is acting perpendicular to a surface.

2 Marks Questions

Q.1 Â An object is suspended with a string which gets stretched. When the object is completely immersed in water, the extension of thread decreases. ExplainÂ  why it happens.

Q.2 Â (a) State the principle on which the working of a hydrometer is based.

(b) A sharp knife is more effective than a blunt knife. Why ?

Q.3 Â What happens when:

(a) Buoyant force exerted by the fluid is greater than the weight of the body?

(b) Buoyant force exerted by the fluid is equal to the weight of the body?

Q.4 Â Why are railway tracks laid on large sized concrete sleepers? Explain.

Q.5 Â An object of 40 N weight when immersed in water losses 10 N weight. Will the object float or sink? Why?

Q.6 Â Two blocks, one of iron and other of wood are immersed in water at same depth. Which one will come upward. Why?

Q.7 Â Define relative density of a substance. Relative density of silver is 10.8. The density of water is 1000 $kg/m^{3}$. What is the density of silver in SI units?

Q.8 Â Which will exert more pressure 100 kg mass on 10${m^2}$ or 50 kg mass on 4 ${m^2}$ ? Give reason.

Q.9 Â (a) Explain why a truck or a motor bus has much wider tyres ?

(b) Why do we feel lighter when we swim?

Q.10 Â Account for the statement "Camel walks easily on sand but it is difficult for a man to walk on sand though a camel is much heavier than a man".

Q.11 Â Differentiate between density and relative density.

Q.12 Â Lead has greater density than iron and both are denser than water. Is the buoyant force on a lead object greater than, or lesser than or equal to the buoyant force on an iron object of the same volume?

Explain your answer giving reason.

Q.13 Â Explain why sheet of paper falls slower than a coin under gravity through air.

Q.14 Â Give one example each where the same force acting on

(a) a smaller area exerts a larger pressure,

(b) a larger area exerts a smaller pressure

Q.15 Â Why does a nail sink in water but a piece of cork floats on it?

Q.16 Â State Archimedes' principle. Write two applications of this principle.

Q.17 Â A body of mass 20 kg is placed on a 2${m^2}$ area. Find the pressure exerted.

Q.18 Â An iron ball weights 11 kg in air and 8 kg when immersed in water. Find its relative density.

Q.19 Â Thrust of 'F' N is exerted on area 2A and thrust of '3F' N is exerted on area A/2. Find the ratio of pressure exerted.

Q.20 Â A boy lying on a mattress, stands up on it. He observes that the mattress is now depressed deeper down. Why does this happen?

Q.21 Â What are fluids? How does upthrust exerted by a fluid on an object immersed in it vary with density of fluid?

Q.22 Â Big trucks and tractors have broad tyres. Why?

Q.23 Â An iron nail sinks in the water. But a ship made of iron floats on water. Why?

Q.24 Â A bag of cotton weighs 10 kg and occupies a volume of 2 ${{\rm{m}}^3}$. Find its density. Express this density in CGS. unit.

Solutions

1. Â The buoyant force exerted by a fluid is equal to the weight of fluid displaced. As a body is lowered in a fluid ,more is the fluidÂ Â  displaced, more is the buoyant force.Â  This buoyant force is maximum when a body is completely immersed in a fluid , The extension of thread keeps decreasing as the net forceÂ  deceases.

2. Â (a) Archimedes Principle : When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluidÂ  displaced by it.

(b) A sharp knife has a smaller area of cross section on which force acts. Thus pressure on sharp knife is more and it is more effective than a blunt knife.

As , ${\rm{ Pressure}}\alpha {1 \over {area}}$

3.Â Â (a) The body rises to the surface of fluid.

(b) The body floats.

4. Â Railway tracks are laid on area on large sized concrete slabs to increase the area on which the weight of train will act and hence decrease pressure on the ground.

5. Â The object will sink as weight of object is greater than the buoyant force.

6. Â The wood block will come up because density of wooden block is less than water, where as iron has greater density than water.

7. Â Relative density is defined as the ratio of density of substance to that of water.

10.8=${{{\rm{Density}}\,{\rm{of}}\,{\rm{silver}}} \over {1000}}$

therefore Density of silver = 10.8 X ${10^3}$ kg/${m^3}$

8. Â P1=${{100} \over {10}}$=10 Pa.

P2=${{50} \over 4}$ = 125 Pa.

The second mass will exert greater pressure.

9. Â (a) Bus or truck have wider tyres as they carry heavier loads. To reduce pressure on the ground, the tyres are kept wider.

(b) Â We feel lighter when we swim due to the buoyant force. Our apparent weight is actual weight.

10.Â Â Camels are much heavier than men but due to their wide feet the pressure exerted on sand is much less, making it easier for them to walk on it.

11. Â Density is defined on mass per unit volume. Its unit kg/${m^3}$.

Relative density is the ratio of density of substance to that of water. It is a unit less quantity.

12. Â Buoyant force depends on the volume of fluid displaced. It a lead and iron object having same volume are immersed in water, both will experience the same buoyant force.

13. Â A sheet of paper has greater surface area, therefore air resistance is more , so it falls slower.

14. Â (a) A man standing on h is feet

(b) A man lying down

15. Â The density of cork is less than water whereas nail has greater density. So cork floats while nail sinks.

16. Â Archimedes Principle states when a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

Application :

1) Designing of ships, submarines

2) Lactometers

17. Â Pressure = ${{{\rm{Force}}} \over {{\rm{Area}}}} = {{20 \times 10} \over 2} = 100\, Pa.$

18. Â Relative Density =${{{\rm{weight}}\,{\rm{of}}\,{\rm{object}}} \over {{\rm{Loss}}\,{\rm{of}}\,{\rm{weight}}\,{\rm{in}}\,{\rm{water}}}}$

= ${{11} \over {11 - 8}} = {{11} \over 3} = 3.07$

19. Â ${P_1} = {F \over {2A}}$

${P_2} = {{3F} \over {A/2}} = {{6F} \over A}$

${{{P_1}} \over {{P_2}}} = {{F/2A} \over {6F/A}} = {1 \over {12}}$

Ratio is 1 : 12

20. Â The mattress is depressed deeper when the boy stands as pressure increase when area on which the weight acts becomes smaller. As pressureÂ $\alpha {1 \over {area}}$ ; the pressure on the mattress increases.

21. Â Fluids are matter that can flow i.e. liquids and gases.

upthrust = weight of fluid displaced

= volume of bodyÂ $\times$ density of fluidÂ $\times$ acc. due to gravity.

Greater the density, greater will be the upthrust.

22. Â Bus or truck have wider tyres as they carry heavier loads. To reduce pressure on the ground, the tyres are kept wider.

23. Â A body sinks if its weight is greater than the buoyant force on it like the nail.
The ship has a large volume immersed in water. So , buoyant force is equalÂ  to its weight. So the ship floats.

24. Â Density =${{{\rm{Mass}}} \over {Vol.}} = {{10kg} \over {2{m^3}}}$

$= {{10 \times 1000\,gm} \over {2 \times 100 \times 100 \times 100\,c{m^3}}}$

$= {1 \over {200}}\,g/c{m^3}$

3 Marks Questions

Q.1 Â Define pressure and state its SI unit. The dimensions of a metallic cuboid are 30 cm x 20 cm x 15 cm and its mass is 30 kg. If the acceleration due to

Q.2 Â (a) Do all bodies immersed in a given fluid experience the same buoyant force? Explain.

(b) A 100=$c{m^3}$ block has a mass of 395 g. Find its relative density. (Density of water = 1 g/$c{m^3}$)

Q.3 Â What is meant by buoyancy? Why does an object float or sink when placed on the surface of a liquid?

Q.4 Â (a) State the SI units of Thrust and Pressure.

(b) In which situation we exert more pressure on ground when we stand on one foot or on both feet? Justify your answer.

Q.5 Â Describe a simple activity to prove that objects of density less than that of the liquid float on it.

Q.6 Â The volume of a bag of mass 1250 g is 150 $c{m^3}$. If this bag is put on water, will it float or sink? Justify your reply. Also, find the volume of water displaced by this bag.

Q.7 Â A hollow plastic ball is taken to the bottom of a trough of water and released there.

(a) What happens to the ball? Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Â

(b) Give reason for this phenomenon.

Q.8 Â State any two daily life phenomena which are based on Archimedes' principle. Discuss the role of Archimedes' principle in industry and defense.

Q.9 Â A box has dimensions 15 cm x 20 cm x 25 cm. Calculate pressure exerted by box if it is rested on a surface at

(a) 15 cm x 20 cm face

(b) 20 cm x 25 cm face

(c) 15 cm x 25 cm face, given mass of box = 20 kg. Arrange the pressure in ascending order of their magnitude.

Solutions

1. Â Pressure is defined as thrust per unit area. Its unit is Pascal.

Pressure =${F\over A} = {{mg} \over {Area}} = {{30\times 10} \over {{{20} \over {100}} \times {{15} \over {100}}}} = {10^4} Pa.$

2. Â (a) Buoyant force experienced by a body depends on volume of bodyÂ  immersed and the density of the fluid. If the volume of the immersed part of bodies is same, theyÂ  will experience the same force.

(b) Â Density of block =${m\over V} = {{395}\over {100}} = 3.95\,g/cm^3$

$R.D.={{Density{\mkern 1mu} of{\mkern 1mu} block}\over {Density{\mkern 1mu} of{\mkern 1mu} water}} = {{3.95} \over 1} = 3.95$

3. Â Buoyancy is the upward force experienced by an object placed in a fluid.

An object floats or sinks when placed on water depending the net force. If the weight is less than buoyant force it will float, and if more then it will sink.

4. Â (a) SI unit of Thrust is Newton and of pressure is Pascal.

(b) We exert more pressure on ground when we stand on one feet than when we stand on both feet because pressure is inversely proportional to theÂ  area on which the thrust acts.

5. Â Take a block of wood and iron of same volume and put then in a liquid. It is seen that wood floats while iron black sinks. It we find the density of wood it is less than the liquid while that of iron is more. Thus, it is proved that objects having less density than liquid float on it.

6. Â Density = ${{1250} \over {150}} = 8.33\,g/c{m^3}$ since the density of bag is greater than water it will sink.

Volume of water displaced = volume immersed x density of water

= 150 Ã— 1 = 150 $c{m^3}$.

7. Â (a) When the ball is released it rises to the surface.

(b) The reason being buoyant force is greater than its weight, so there is a net force in the upward direction.

8.Â Â (1) Floating of boatÂ

(2) Rising of helium filled balloon in air.

In industry Archimedes principle helps in testing purity of materials and designing ships and submarines .

9. Â (a)Â  ${P_a} = {{20\times 10} \over {{{15} \over {100}}\times {{20} \over {100}}}} = 6666.67\,\,{P_a}$

(b)Â  ${P_b} = {{20\times 10} \over {{{20}\over {100}}\times {{25}\over {100}}}} = 4000{P_a}$

(c) ${P_c} = {{20\times 10} \over {{{15}\over {100}}\times {{25}\over {100}}}} = 5333.33{P_a}$

Therefore, Â ${P_b} < {P_c} < {P_a}$

5 Marks Questions

Q.1 Â (a) State two factors on which the magnitude of buoyant force acting on a body immersed in a fluid depends.

(b) Will buoyant force exerted by a liquid increase if its volume is increased?

(c) Name the devices based on Archimedes' principle.

Q.2 Â State Archimedes' principle. How will you verify it experimentally?

Q.3 Â What is upthrust? What are the quantities that can vary upthrust? How does it account for the floating of a body? When a partially immersed body is pressed down a little, what will happen to the upthrust?

Solutions

1. Â (a) The two factors on which the buoyant force depends is density of liquid, and volume of immersed body.

(b) Yes.

(c) Lactometer , Hydrometer

2. Â Archimedes Principle states that when a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

Experimental verification of Archimedes Principle :Â

Tie a block by a string and suspend it on the a spring balance. Measure the weight of block say W1.
TakeÂ  an overflow flask and a measuring cylinder. Fill the overflow jar to the brim with water. GraduallyÂ  immerse the block into the water . As the block goes inside the water, water will overflow to the measuring jar. Read the weight of block now say W2 .

Measure the water overflowed.

Calculate the weight of water by using formulas= $\rho \times V \times g$ ,where $\rho$ is density of water, V the volume of water overflowed, g the acceleration due to gravity.
You will find that the loss in weight (W1- W2) is equal to weight of water displaced.

3. Â The upthrust can vary by changing volume of body immersed or density of fluid.The upward force exerted by a fluid is called upthrust. Due to upthrust the apparent weight of the body can vary. It the upthrust is equal to the weight ofÂ  the body, the body will float.Â When a partially immersed body is pressed down, upthrust increases.

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