__FLOATING AND SINKING__

- State how a hydrometer may be used to test whether a car battery is fully charged.
- Determine the density of glass that weighs 0.5N in air and 0.3N in water.
- A mass of 120g half immersed in water displaced a volume of 20cm
^{3}. Calculate the density of the object. - A solid displaced 5.5 cm
^{3 }of paraffin when floating and 20cm^{3}. Calculate the density of the object. - The figure below shows a cube of a certain wood whose density is the same as that of water. The cube is held on the surface of the water in a long cylinder. Explain what happens to the cube after it is released.
- A right angled solid of dimensions 0.02m by 0.02m by 0.2m and density 2,700kg/m
^{3}is supported inside kerosene of density 800kg/m^{3}by a thread which is attached to a spring balance. The long side is vertical and the upper surface is 0.1m below the surface of the kerosene. - i) Calculate the force due to the liquid on the lower upper surface of the solid.
- ii) Calculate the up thrust and determine the reading on the spring balance.
- A solid copper sphere will sink in water while a hollow copper sphere of the same mass may float. Give a reason for this.
- A uniform plank of wood is pivoted at its centre. A block of wood of mass 2kg is balanced by a mass of 1.5 placed 30cm from the pivot as shown.

- i) Calculate the distance X
- ii) When the same block of wood is partially immersed in water, the 1.5kg mass need to be placed at 20cm from the pivot to balance it. Calculate the weight of the water displaced.
- A block of glass of mass 250g floats in mercury. What volume of the glass lies under the surface of the mercury? (Density of mercury is 13.6 x 10
^{3}) - When a piece of metal is placed on water, it sinks. But when the same piece of metal is placed on a block of wood, both are found to float. Explain this observation.
- a) State the law of floatation.
- b) Figure 13 shows a simple hydrometer.

- i) State the purpose of the lead shots in the glass bulb
- ii) How would the hydrometer be made more sensitive?

iii) Describe how the hydrometer is calibrated to measure relative density.

- c) Figure 14 shows a cork floating on water and held to the bottom of the beaker by a thin thread

- i) Name the force acting on the cork.
- ii) Describe how each of the forces mentioned in (i) above changes when water is added into the beaker until it fills up.
- The ball B shown below has a mass of 12kg and a volume of 50litres. It is held in position in sea water of density 104 kgm
^{-3}by a light cable fixed to the bottom so that^{4}/_{5}of its volume is below the surface determine the tension in the cable. - A balloon of volume 1.2×10
^{7}cm^{3}is filled with hydrogen gas of density 9.0 x 10^{-5}/g/cm Determine the weight of the fabric of the balloon. - A boat whose dimensions are equivalent to those of a rectangular figure of 5m long by 2m wide floats in fresh water. If this boat sinks 10cm deeper as a result of passengers climbing on board, determine the total weight of these passengers.
- One fifth of the volume of an iceberg stands above the water surface. If the density of the seawater is 1.2g/cm
^{3}, determine the density of iceberg. - A hydrometer of mass 10g is placed in paraffin of density 0.8g/cm
^{3}. Determine the length of the paraffin if its bulb has a volume of 4cm^{3}and its stem has a cross section area of 0.5 cm^{2} - An object of mass 50g floats with 20% of its volume above the water surface as shown below. The tension in the string is 0.06N.

- a) Calculate the up thrust experienced by the object.
- b) Volume of water displaced.
- c) The density of the object
- d) What would happen if the string was cut?
- A piece of marble of mass 1.4kg and relative density 2.8 is supported by a light string from a spring balance. It is then lowered into the water fully. Determine the up thrust.
- The block of wood of mass 80g is pulled just below the water surface by a piece of copper of density 9g/cm
^{3}using a string of negligible weight. What is the mass of the piece of copper?

- If the body weight 1.80N in air and 1.62N when submerged in a liquid of relative density 0.8, find the volume of the solid.

The density of the solid

- (a) State the law of flotation.

(b ) Figure 10 shows a rectangular metal block of density 10500 kgm3 and dimensions 30 cm x 20 cm x 20 cm suspended inside a liquid of density 1200 kgm^{-3} by a string attached to a point above the liquid. The three forces acting on the block are the tension T, On the string, the weight W, of the block and the upthrust, U due to the liquid.

(i) Write the expression relating T, W and U when the block is in equilibrium inside the liquid.

(ii) Determine the weight, W of the block

(iii) Determine the weight of the liquid displaced by the fully submerged block.

(iv) Hence determine the tension, T in the string.

(c) A certain solid of volume 50 cm^{3 }displaces 10 cm^{3 }of kerosene (density 800 kgm^{3}) when floating. Determine the density of the solid.

- a) An object weighs 2.04N in air, 1.64N in water and 1.72N when fully immersed in an unknown liquid. Calculate the density of the unknown liquid.
- b) Give a reason why a small ball-bearing made of steel sinks in water while a large ship of the same material floats on water.
- c) The figure 8 below is a bouy B of volume 80 litres and of mass 20Kg. It is held in position in sea water of density 1.04×10
^{3}Kgm^{-3}by a light string fixed to the bottom so that 0.73 of its volume is below the surface of water.

Determine the tension T in the string.

- d) Figure 9 shows a hydrometer which is suitable for measuring densities of liquids range between 1.0 and 1.2gcm
^{-3}

On the diagram, indicate against A and B the level corresponding to these extreme range of densities.

- e) Figure 10 shows a wooden cube whose density is the same as that of water. The cube is held on the suface of water.

State and explain what would happen to the cube on releasing it.

- (a) Figure 9 shows the same metal block weighed in air, water and liquid. . Given that the reading of the level of water becomes 75cm
^{3 }when the metal is fully immersed,

Determine:

(i) Density of the metal

- ii) Water level before the solid was immersed.

iii) Explain why the spring balance gives different reading in figure 9 (b) and 9 (c) with the same metal block.

(b) Figure 10 below shows a uniform plank of length 6.0m acted upon by forces shown. If the plank has a weight of 10N, determine the weight of W given that volume of metal block is 5000cm^{3}, density of water = lg/cm3

- (a). State Archimedes’s Principle .

b). A during bell of weight 60,000N and volume 2m^{3 }is to be raised from the bottom of

the sea. If the density of sea water is 1024kg/m^{3}, calculate:

(i) the mass of sea-water displaced by the bell.

(ii) The force a crane must first exert to just lift the bell from the sea-bed.

(c). The figure below shows a bock of wood of dimension 16cm x 8cm 2cm floating with

¾ of its size submerged in a liquid.

Beaker |

Balance |

Liquid L |

During the experiment with the following set-up above, the following results were obtained.

-Initial reading of the Toppan balance with empty beaker = 22g.

-Final reading of the top pan balance = 176g.

Use the above results to determine:

(i). the density of the block

(ii). The density of the liquid.

- (a) A piece of sealing wax weighs 3N in air and 0.22N when immersed in water. Calculate:

(i) Its relative density.

(ii) Its apparent weight in a liquid of density 800 kgm^{-3}.

(b) The figure below shows a uniform beam one metre long and weighing 2N kept in

horizontal position by a body of weight 10N immersed in a liquid.

Determine the upthrust on the load.

- A bubble of air has a diameter of 2.0 mm when it is 0.5m below the water surface of a boiler. Calculate the diameter of the bubble as it reaches the surface, assuming that the temperature remains constant.

(Take g = 10Nkg^{-1} density of water = 10^{3}kgm^{-3} and atmospheric pressure = 10^{5}Mn^{-2}

- (a) State the Archimedes principle

(b) The figure below shows a block of mass 25g and density 200kg/m^{3} submerged beam by means of a thread. A mass of 2g if suspended form the beam as shown in the figure below

(i) Determine the up thrust force acting on the block

(ii) Calculate the density of the liquid

(c) A rectangular block of dimensions 4m x 3m x 2m is tethered to the sea bed by a wire. If the density of the material making the block is 0.67g/cm^{3} and density of water is 1.1g/cm^{3}, calculate: (i) Up thrust force on the block

(ii) Tension on the wire

- Explain why a needle can be carefully made to float in pure water but sinks if a detergent is added.
- (i) State the law of floatation.

(ii) The fig. below shows a floating object of volume 40,000 cm^{3} and mass 10g. It is held as shown in water of density 1.25g/cm^{3} by a light cable at the bottom so that ¾ of the volume of the object is below the water surface. (Assume that up thrust due to air is negligible)

Figure 11 |

Cable |

(iii) (I) Calculate the volume of the object under water.

(II) State the volume of water displaced by the object.

(III) Calculate the weight of water displaced.

(iv) Determine the tension in the cable

(v) Calculate the density of the object.

- (a) A trolley is being pulled horizontally from a ticker-tape timer. The figure below shows part of the ticker-tape.

Figure 12 |

(i) Find the average velocity, **u**, at the section marked **A**.

(ii) Find the average velocity, **V** at the section marked **B**.

(iii) Find the acceleration of the trolley between **A** and **B**.

(b) If the mass of the trolley is 500g, determine the resultant force which acted on the trolley that caused the acceleration.

- (a) State Archimedes’ principle

(b) (i) Draw a clearly labelled diagram of common hydrometer which is suitable for measuring the densities of liquids varying between 1.0 and 1.2 g/cm^{3}. Show clearly the marks indicating 1.0, 1.1 and 1.2 g/cm^{3}.

(ii) State the principle upon which the instrument’s use depends

(c) A concrete block of volume** V** is totally immersed in sea water of density **J.**Write an

expression for the upthrust on the block

- (a) Define the term relative density

(b) The diagram below shows a wooden log 12m long, density 800kg/m^{3} and cross-sectional area 0.06m^{2 }floating upright in sea water of density 1.03g/cm^{3}, such that a third of it is covered by water.

A= 0.06m^{2} |

(i) Determine the weight of the block

(ii) The up-thrust on the block

(iii) The minimum weight that can be placed on the block to just make it fully submerged

Sinker |

water |

Cork |

Sinker |

Cork |

Water |

(c) The following set-up was then used by a student to determine the relative density of a cork

During the experiment, the following measurements were taken:-

– Weight of sinker in water = **w _{1}**

– Weight of sinker in water and cork in air = **w _{2}**

– Weight of sinker and cork in water = **w _{3}**

(i) Write an expression for the up thrust on cork

(ii) Write an expression for the relative density of the cork

- (a) State the law of floatation

(b) The diagram ** figure 11** below shows a block of wood floating on water in a beaker. The set-up is at room temperature:-

* fig. 11*

The water in the beaker is warmed with the block still floating on it. State and explain the

changes that are likely to occur in depth **x**

(c) The diagram ** figure 12** below shows a balloon which is filled with hot air to a volume of 200m

^{3}. The weight of the balloon and its contents is 2200N.

*fig. 12*

(i) Determine the upthrust on the balloon (density of air 0.0012g/cm^{3})

(ii) The balloon is to be balanced by hanging small rats each of mass 200g on the lower end of the rope. Determine the least number of rats that will just make the lower end of the rope touch the ground.

- (a) State Archimedes’s principle

(b) A rectangular brick of mass 10kg is suspended from the lower end of a spring balance and gradually lowered into water until its upper end is some distance below the surface

(i) State and explain the changes observed in the spring balance during the process

(ii) If the spring reads 80N when the brick is totally immersed, determine the volume of the brick. (Take density of water = 1000kgm^{-3})

(c) The figure below shows a hydrometer

Lead shots |

** Explain:**

(i) Why the stem is made narrow

(ii) Why the bulb is made wide

(iii) Why the lead-shots are placed at the bottom

- (a) State the law of floatation

(b) The diagram below shows a wooden block of dimensions 50cm by 40cm by 20 cm held in position by a string attached to the bottom of a swimming pool. The density of the block is 600kgm^{-3}

(i) Calculate the pressure in the bottom surface of the block

(ii) State the** three** forces acting on the block and write an equation linking them when the block is stationary

(iii) Calculate the tension on the string

- A block of glass of mass 250g floats in mercury. What volume of glass lies under the surface of Mercury? Density of mercury is 13.6 x 10
^{3 }Kg/m^{3 } - a) State the law of floatation
- b) A balloon of negligible weight and capacity 80m
^{3}is filled with helium of density 0.18Kgm^{-3}. Calculate the lifting force of the balloon given that the density of air = 1.2Kgm^{-3} - c) A piece of glass has a mass of 52g in air, 32g when completely immersed in water and 18g when completely immersed in an acid. (Take: density of water = 1g/cm
^{3})

Calculate:

- i) Density of glass
- ii) Density of the acid

- (a) Fig 6 below shows a uniform plank of weight 20N and length 1.0m balanced by a 0.5kg mass at a distance x from the pivot point O.

Figure 6

Determine the value of x

(b) When the block is completely immersed in water the pivot 0 must shift by 0.05 m to the left for the system to balance. The density of water is 1000 kgm^{-3}.Determine:

(i) The upthrust U on the block.

(ii) The volume of the block.

- a) The figure 9 below shows a ball of 15kg and volume 0.06m
^{3}held in position in sea water held by a chain and block of lead. The density of the sea water is 1.04gcm^{-3}and the ball is held half its volume below the surface of the sea water.

Fig 9

Lead block |

Ball |

- a) What volume of sea water is displaced by the ball?
- b) Determine the weight of the chain and block of lead which keeps the ball in its position
- c) If the ball becomes separated from the chain and floats by itself in sea water, what volume of the ball will submerge?
- d) i) State
**two**factors that determine the magnitude of centripetal force acting on a body moving uniformly in a circular path. (2 mks) - ii) A cyclist negotiating a corner at a high speed leans inwards in order to successfully pass. Explain how this action enables him to negotiate.
- (a) State Archimedes Principle

(b) The figure below shows a block of mass 50g and density 2000kg/m^{3} submerged in a certain liquid and suspended from uniform horizontal beam by means of a string. A mass of 40g suspended from the other end of the beam puts the system in equilibrium.

(i) Determine the upthrust force acting on the block.

(ii) Calculate the density of the liquid

(iii) Calculate the new balance point of the 50 g mass (the 40g mass remains fixed) if the liquid was replaced with one whose density was 1500Kg/m^{3}

- a) State Archimedes principle.

- b) The figure below shows a rectangular block of height 4cm floating vertically in a beaker containing two immiscible liquid A and B. The densities of the liquid are 8000 kg/m 3 and 12000 kg/m3 respectively.

The cross sectional area of the block is 2cm^{2}

Determine

- The weight of the liquid A displaced by the block
- The weight of the liquid B displaced by the block

- The mass of the block

- The density of the block
- A body weighs 3.8 N in air and 2.8 N when fully immersed in water. Find the relative density of the body (Density of water is g/cm 3)
- State the special features of a hygrometer
- (a) State Archimedes’ principle.

(b) A solid Y weighs 40N in air, 30N when in water and 35N in liquid X. Find the density of;

(i) Solid Y

(ii) Liquid X

(c) A simple hydrometer is set up with a test – tube of mass 10g and length 12cm with a flat base and partly filled with lead shots. The test tube has a uniform cross-sectional area 2.0cm^{3} and 10cm of its length is under water as shown in the figure below.

(i) Taking the density of water as 1000Kg/m^{3}. Calculate the mass of the lead shots in the test tube.

(ii) The mass of the lead shots to be added if it has to displace an equal volume of a liquid of density 1.25g/cm^{3}.

- (a)
**State**Archimede’s principle

(b) A cork and a stone are both held under water and released at the same time.

- State the observation that would be made
- Explain the observation above

(c) A wooden block measures 2cm by 5cm by 10cm floats in water with its length vertical. if three quarters of its length is submerged, determine;

- The density of the block
- The volume of the block remaining above the surface when floating in a liquid of density 800kgm
^{-3}

(d) In an experiment to determine the relative density of methylated spirit by applying Archemedes principle, the follwing results were obtained.

Mass (g) | 100 | 150 | 200 |

Weight in air (N) | 1.00 | 1.50 | 2.0 |

Weight in water (N) | 0.88 | 1.32 | 1.76 |

Apparent loss in weight (N) | |||

Weight in methylated spirit (N) | 0.91 | 1.36 | 1.82 |

Apparent loss in weight (N) |

- Fill in the blank spaces in the table
- On the same axes, plot a graph of upthrust (y-axis) against weight in water; for both water and methylated spirit
- Determine the gradient of each;stating the significance of the gradients.

- a) State Archimedes principle.
- b) The diagram below shows two bodies hanging from the 30cm mark and the 80cm mark of a uniform metre rule. One of the bodies of mass 5kg and volume 0..01 m
^{3}is immersed in a liquid.

Figure 10

If the system is in equilibrium, calculate the density of the liquid.

- c) A balloon used to carry instrument for meteorological department up into the atmosphere has a capacity of 30 m
^{3}and is filled with hydrogen. The weight of fabric of balloon is 30N.

(Determine of hydrogen is 0.089Kgm^{-3} and of air is 1.29 Kg m^{-3} , g = 10Nkg^{-1})

- State the law of floatation
- A solid metal block cross-section area and of density is fully immersed in water , supported by a spring balance

- A part from the weight , state and indicate the direction of any two forces acting on the metal block
- If the upward force acting on the bottom face is ,Calculate the volume of the block
- Calculate the apparent weight of block in water

- c) What is purpose of lead shot in hydrometer?
- A hot air balloon is tethered to the ground on a windless day as shown in figure 3

The envelope of the balloon contains 1200m^{3} of hot air of density 0.8kg/m^{3}. Mass of the empty balloon is 400kg. Density of the surrounding air is 1.3kg/m^{3}. Calculate the tension in the rope holding the balloon on the ground

- a) State the law of flotation
- b) A flat test tube containing lead shots is immersed in a fluid, where it floats as shown

(i) What is the use of the lead shots?

(ii) The following readings were obtained for total mass M, of the test tube and lead shot and the depth, h of the test tube immersed as lead shot was added to the tube.

M/g | 48 | 55 | 60 | 65 | 73 | 77 | 84 |

h/cm | 8 | 9 | 10 | 11 | 12 | 13 | 14 |

Plot a graph of M against depth

(iii) From the graph find the depth immersed when M is 90g

Use this result to find area of the base of the tube (density of liquid =1.2g/cm^{3})

(iv) State one use of a hydrometer

- The diagram below shows a car acid hydrometer.

** **(i) Indicate on the diagram above the minimum and the maximum measurement to be taken.

(ii) State the reason why the bulb is wide.

- a) State the law of floatation.
- b)
**You are provided with the following:-**

– A block of wood

– A spring balance

– Thin thread

– Overflow can

– A small measuring cylinder

– Some liquid

With the aid of a labeled diagram describe an experiment to the law of floatation.

- c) A block of length 80cm cross sectional area of 3.0cm
^{3}and density 1300kg / m^{3}is completely immersed in a liquid of density 1030 kg/ m^{3}.

**Determine:-**

(i) The mass of the block.

(ii) The weight of the block in the liquid.

- a) State the law of flotation
- b) A hydrometer is floating in a liquid at temperature of 18
^{0}If the temperature of the liquid is raised to 50^{0}C state the observation made - c) A cylindrical beaker of uniform X – sectional area of 50cm
^{2}and height 12cm floats in water with one third of its volume immersed. A liquid Q is poured into the beaker until it completely sinks. Density of water = 1.og/cm^{3}. Density of liquid Q = 1.25g/cm^{3}

Determine

- i) Weight of beaker
- ii) Upthrust of water before the beaker is completely immersed

END |

iii) The volume of liquid Q used

- (a) Sate the law of floatation.

(b) The figure below shows a piece of cork held with a light thread attached to the bottom of a beaker. The beaker is filled with water.

- Indicate and label on the diagram the forces acting on the cork.
- Write an expression showing the relationship between the forces above.
- If the thread breaks, name another force that will act on the cork.
- A solid displaces 8.5cm
^{3}of liquid when in a certain liquid and 11.5cm^{3}when fully submerged in the same liquid. The density of the solid is 0.8g/cm^{3}. determine:-- The upthrust on the solid when floating.
- The density of the liquid.
- The upthrust on the solid when fully submerged.

- A solid of mass 100g and density 2.5g/cm
^{3}weighs 0.5N when totally submerged in a liquid. Determine the density of the liquid. - a) State Archimedes’ principle
- b) A cube of side 12cm is completely immersed in a liquid of density 800kgm
^{-3}so that the top surface of the cube is horizontal and 20cm below the surface of the liquid as shown in the figure below.

Figure 8

Fig 8

Calculate the pressure due to the liquid on the cube.

- i) at a depth of 20cm
- ii) at a depth of 32cm
- c) Hence calculate the force due to the pressure difference between the top surface and the bottom of the cube
- a) i) State Archimedes’s Principle.
- ii) An object weighs 1 .04N in air, 0.64N when fully immersed in water and 0. 72N when fully immersed in a liquid. If the density of water is 1000 kgm
^{-3},find the density of the liquid. - b) i) State the law of floatation
- ii) Give a reason why a steel rod sinks in water while a ship made of steel floats on water.
- Figure 13 shows a buoy, B, of volume 40 litres and mass 10 kg. It is held in position in sea water of density 1.04gcm
^{-3}by a light cable fixed to the bottom so that 3 of the volume of the buoy is below the surface of the sea water. Determine the tension T in the cable.

** Fig.13**

b(iii) The figure below shows a diagram of a hydrometer which is suitable for measuring the densities of liquids varying between 1.0 and 1.2g cm^{-1}

B |

A |

On the diagram indicate the label corresponding to 1.0 and 1.2 g/cm^{3}

- a)A student was provided with the following

Density bottle; beam balance, water and liquid x

Describe how you would use the above to determine the relative density of liquid x.

- b) In the figure below a block with graduated side and dimensions. 10cm X 2 cm X 16 cm is just about to be lowered into a liquid in a Eureka can.

Block |

Wooden block |

Compression balance |

Beaker |

Eureka can |

During the experiment the results were recorded as

(i) The block floated with 75% of it submerged.

(ii) Initial reading of compression balance 0.0g

iii) Final reading of compression balance 160g.

Use the above results to determine the density of the block.

- a) State the law of floatation.
- b) A body weighs 40N in air, 30N when in water and 35N when in liquid X. Find the relative density of liquid X.
- c) A simple hydrometer is set up with a test — tube of mass 10g and length 12cm with a flat base and partly filled with lead shots. The test tube has a uniform Cross — Sectional area 2.0cm
^{2 }and 10cm of its length is under water as shown in the figure below.

(i) Taking the density of water as l000Kg/m^{3}. Calculate the mass of the lead shots in the tube.

(ii) The mass of the lead shots to be added if it has to displace an equal volume of a liquid of

density 1.25g/cm^{3}.

- (a) State the law of floatation. (b) You are provided with the following apparatus:

– A block of wood

– A spring balance

– Thin thread

– Overflow can

– A small measuring cylinder

– Some water.

Using the apparatus above, describe an experiment to verify the law of floatation.

(c) The relative density of a solid is 2.4. Determine the upthrust it experiences when floating

on water if the weight is 200N in air.

(d) Figure 3 below shows a hydrometer.

** Fig 3 **

(i) State the purpose of the part marked C.

(ii) Identify the higher value between the reading at A and B.

- a) State Archimedes’s principle.
- b) The figure below shows a black of mass 25g and density 2000kg/m
^{3}submerged in a certain liquid and suspended from a uniform horizontal beam by means of a thread. A mass of 2g is suspended from the beam as shown.

- i) Determine the thrust force acting on the liquid.
- ii) Calculate the density of the liquid.
- c) The rubber used to make a balloon weighs 0.1kg.The balloon is inflated to a volume of 0.5m
^{3}with hydrogen whose density is 9.0 x10^{-2}Kg/m^{3}.What is the maximum load the balloon can lift. (Density of air=1.3Kg/m^{3}) - a) State Archimedes’s principle.
- b) A student was provided with water in a beaker, a spring balance, a metal block, a cork and a string. Using the arrangements shown in figure 9 she recorded the following results

Fig 9

Weight of cork in air = W_{1}

Weight of cork in air and metal in water = W_{2}

Weight of both cork and metal in water = W_{3}

- i) Write an expression for the upthrust on the cork in water.
- ii) Derive an expression for the relative density of the cork.
- Apiece of wax of mass 380g and volume 400cm
^{3}is kept under water by tying with a thin thread to a piece of metal. Determine the tension in thread. - (a) State the law of floatation. (b) Figure 12 shows a piece of cork held with a light thread attached to the bottom of a beaker. The beaker if filled with water.

Water |

Cork |

Fig. 12 |

(i) Indicate and label on the diagram the forces acting on the cork.

(ii) Write an expression showing the relationship between the forces.

(c) A solid displaces 8.5cm^{3 }of liquid when floating on a certain liquid and 11.5 cm^{3} when fully submerged in the liquid. The density of the solid if 0.8g/cm3. determine:

(i) Up thrust on the solid when floating.

(ii) Density of the liquid.

- a) State the law of flotation.
- b) A rectangular block of cross section area 0.08m
^{2}is immersed in a liquid of density 1200kgm^{-3}. The top and the lower surfaces are 20cm and 80cm below the surface of the liquid respectively - i) What is the downward force on the top of the block?
- ii) Calculate the upthrust on the block.
- c) A block of glass of mass 0.25kg floats in mercury of density 1.36 x 10
^{4}kgm^{-3}. What volume of the glass lies under the surface of mercury? - d) The weight of a cube in air is 0.5N. When immersed in water, it weighs 0.44N and in oil weighs 0.46N. Calculate the relative density of the oil.
- a) State the law of flotation.
- b) What determine the depth to which a body sinks in a liquid?
- c) A student constructed a hydrometer for use in milk industry. State the modification he can make to increase the sensitivity of the hydrometer.
- d) Name this type of hydrometer.
- e) State the Archimedes Principle.
- e) A balloon of volume 9.0m
^{3}is filled with hydrogen of density 0.18kg/m^{3}and held in position as shown. If it floats in air of density 1.3kg/m^{3}and the weight of the balloon envelop 45N is calculate the tension T.

T

- f) A solid object weighs 90N when suspended in air and 84N when immersed in water. When fully submerged in an acid it weighs 76N. Determine the relative density of the acid.
- (a) A test tube of uniform cross-section is loaded so that it can float upright in water figure 5 below.

mm scale |

Water |

Lead shots |

Fig 5

(i) Describe how the test tube above may be catibrated to measure densisty of liquid .

(ii) On the same diagram indicate the position of the Zero mark on the mm scale if it is calibrated to measure density.

(iii) Give a reason for the position of the zero mark indicated in (ii) above. (2mks)

(b) In an experiment to determine the density of a liquid a uniform metal cylinder of cross-section area 6.2cm^{2} was hang from a spring balance and lowered gradually into the liquid. The upthrust was determined for various submerged lengths. The results obtained are shown on the graph figure 6. below.

Fig 6

Use the graph to

(i) Determine the upthrust when the cylinder is fully immersed if it length is 10.5 cm.

(ii) Determine the density of the liquid.

- (i) State the law of floatation

(ii) A balloon made up of a fabric weighing 80N has a volume of 1x 10^{7}cm^{3}. The balloon is filled with hydrogen of density 0.09 Kgm^{-3}.Calculate the greatest weight, in addition to that of the hydrogen and its fabric which the balloon can carry in air of average density 1.25kgm^{-3}.

(b) The diagram below shows the same metal block weighed in air,water and liquid **X**

Liquid X |

0.7N |

0.8N |

0cm^{3} |

65cm^{3} |

0.72N |

Water |

(i) Calculate the density of the metal.

(ii) Water level before the solid was immersed.

(ii) Density of the liquid **X**

- a) State the law of floatation.
- b) A cylindrical block of wood has a radius 3.5 cm and height 10cm. if floats vertically in a beaker

r=3.5 cm |

containing two immiscible liquids A and B. The densities of the liquids are 0.8g cm^{-3} and 1.2 gcm^{-3} respectively.

4cm |

5 cm |

Liquid A |

Wooden block |

Liquid B |

- i) Determine the mass of the liquid A displaced by the block.
- ii) the mass of liquid B displaced by the block

iii) The density of the block.

(c) Calculate the pressure of the liquid at the depth of 9cm

- a) State the law of flotation
- b) A piece of wood floating with three fifth of its volume immersed in water .What is the density of the wood (density of water 1000kg/m
^{3}) (2mks) - c) A metal block of mass 3kg and volume 500cm
^{3}is hang at the 10cm mark of a uniform meter rule and then is completely submerged in water in a beaker as shown in he diagram below.

**Figure 9**

- i) Show all the force acting on the metal block
- ii) If the rule is pivoted at the 50cm mark determine the point x at which a 50N weight should be placed 50 as to balance it (density of water =1000kg/m
^{3},g=10N/kg) - (a) Define the relative density of a solid

(b) In an experiment to determine the relative density of liquid A, the following set up was used.

100g |

y |

x |

y |

Stand |

Metre Rule |

100g mass |

Liquid A |

The distance x of the mass in liquid A was measured for various length, y of an identical mass of equilibrium and a graph of y against x was drawn as shown in the grid below.

(i) Determine the gradient, S, of the graph.

(ii) If S = , where F is the apparent weight of mass in liquid A and W is the actual weight of the mass. Calculate the value of F and the up thrust u.

(iii) Determine the relative density of the liquid a, given that the weight of the 100g mass

in water was 0.9N.

(c) A balloon’s fabric weighs 10N and has a gas capacity of 2M^{3}. If the gas in the balloon weighs 2N and air has density 1.29kg/m3, Find the resultant force on the balloon when it is floating in air.

- a). State the law of flotation

b). Figure below shows a rectangular bloc of height 10cm floating vertically in a beaker containing two immiscible liquid A and B of densities 800kg/m^{3} and 1000kg/m^{3} respectively. The dimension of the block is 3cm long by 2cm wide and 10 cm high.

2cm |

5cm |

3cm |

Liquid A |

Liquid B |

Fig 9 |

If the length of the block in liquid A is 5cm and that of the block in liquid B is 3cm. Determine

- The weight of liquid A displaced
- Weight of liquid B displaced

- Density of rectangular block

- Explain why a hollow metal sphere floats on water while a solid metal sphere of the same material sinks in the water.