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  • kcse form 2 mathematics questions

A u-tube vertically holds two liquids L1 and L2 as shown in the figure below

17/10/2021

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A u-tube vertically holds two liquids L1 and L2 as shown in the figure below
A u-tube vertically holds two liquids L1 and L2 as shown in the figure above

​(a) Mark accurately the point  in liquid L2 that is at the same pressure as point P (1mk)

​AT the same level as O in the right limb

(b) Determine the number of times L1 is denser than L2 (2mks)

Determine the number of times L1 is denser than L2



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An object  weighs 2.6 N in air and 2.2N when completely immersed in water. Determine the relative density of the object

16/10/2021

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​An object  weighs 2.6 N in air and 2.2N when completely immersed in water. Determine the relative density of the object (2mks)

Solution

Picture

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K.C.S.E Physics Q & A - MODEL 2017PP1QN17

28/7/2020

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K.C.S.E Physics Q & A - MODEL 2017PP1QN17

​(a) State the law of flotation. 
(b) Figure 6 shows two solids W and X made of the same material and immersed in water.
Picture
​(i) State with a reason which one of the containers experiences a greater upthrust.
(ii) Solid W weighs 12 N in air, 2 N ¡n water and 4 N in another liquid. Determine the density of the other liquid. 
(c) Figure 7 shows two identical wooden blocks each of mass 0.2 kg suspended in water by two strings M and N.
Picture
​Given that the upthrust on each block is 3.2 N, determine the tension in string;
(i) M, 
(ii) N. 
(d) State any one application of hydrometers. 
answers
​(a) A floating body displaces its own weight of the fluid in which it  floats.
Picture
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K.C.S.E Physics Q & A - MODEL 2014PP1QN19

23/7/2020

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K.C.S.E Physics Q & A - MODEL 2014PP1QN19

Figure 11 shows a test—tube whose cross-sectional area is 2 cm2 partially filled with lead shot floating vertically in water.

Picture

(Take gravitational acceleration as 10 ms-2 and density of water p as 1 g cm3)
(a) (i) Determine the:
I volume of the water displaced;
II weight of water displaced.
(ii) State the combined weight of the test—tube and the lead shot.
(iii) Determine the length of the test—tube that would be submerged in a liquid of density 0.8 g cm3
. (b) The set tip in figure 11 can be used as a hydrometer to measure densities of liquids.
State how such a hydrometer would be improved to measure small differences in densities of liquids.

answers
Picture
Picture
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K.C.S.E Physics Q & A - MODEL 2013PP1QN18

22/7/2020

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K.C.S.E Physics Q & A - MODEL 2013PP1QN18

​(a) Figure 12 shows a weighing balance on which a beaker containing some water is placed. The reading on the balance is 2.80 N. A metal block weighing 2.7 N is suspended from a spring balance
Picture
​(i) State what is observed on the spring balance and the weighing balance, as the metal block is gradually lowered into the water.
(I) Observation on spring balance. 
(II) Observation on weighing balance. 
(ii) Explain the observation made on the spring balance in (I).
(iii) When the metal block is fully immersed in the water, the reading on the spring balance is found to be 2.46 N. Determine the:
(I) reading on the weighing balance. 
(II) density of the metal.
(c) Figure 13 shows a hydrometer with a thin stem floating in water in a beaker.
Picture
State with a reason what is observed on the hydrometer when the temperature of the water is raised.
answers
(a) (i) (I) - Reading decreases on spring balance;
(II) - Reading on weighing balance increases.
(ii) As the block is lowered, upthust increases; and hence it apparently weighs less;
Picture
(c) The hydrometer sinks more;
The density of the water is reduced;
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K.C.S.E Physics Q & A - MODEL 2012PP1QN18

21/7/2020

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K.C.S.E Physics Q & A - MODEL 2012PP1QN18

​(a) Figure 12 shows a set up used to determine the mass of a solid S. The rod is pivoted at its centre of gravity C.
Picture
​(i) State two measurements that need to be made to determine the mass of solid S. 
(ii) Write an expression to show how the measurements in (i) above are used to obtain the mass of S. 
(b) Figure 13 shows a log of wood of mass 20 kg submerged in water in a pond and held in position by a string fixed to the bottom of the pond.
Picture

Given that the density of water is 1000 kgm3 and that of wood is 800 kgm3, determine the; (i) Volume of the log. (ii) Upthrust on the log. (iii) Tension in the string.

answers
Picture
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K.C.S.E Physics Q & A - MODEL 2011PP1QN019

19/7/2020

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K.C.S.E Physics Q & A - MODEL 2011PP1QN019

​(a) State the condition necessary for a body to float in a fluid. 
(b) A ship made of steel is observed to float on water yet the density of steel is approximately eight times that of water. Explain this observation. 
(c) Figure 17 shows three stages of an experiment to determine relative density of cork which normally floats on water. To make it sink, a sinker is hung below the cork.
Picture
​In (1) a spring balance is used to measure the weight W of the cork in air.
In (II) the spring balance is used to measure the apparent weight W1, when only the sinker is submerged in water.
In (Ill) the spring balance is used to measure the apparent weight W2 when both the cork and the sinker are submerged.
The following observations were made.
W = 0.08N
W = 0.60N
W2 = 0.28N
Use this information to determine the:
(i) Upthrust on cork. 
(ii) relative density of cork. 
(d) Figure 18 shows parts of a simple submarine, a ship that can travel both on water and under water.
To do this water is pumped in or out of the ballast tanks.
Picture
​Explain how the tanks are used to change the depth of the submarine.
answers
Picture
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K.C.S.E Physics Q & A - MODEL 2011PP1QN07

19/7/2020

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K.C.S.E Physics Q & A - MODEL 2011PP1QN07

​Figure 6 shows a small toy boat floating on water in a basin. X and Y are two points near the toy.
Picture
​When a hot metal rod is dipped into the water at point X, the toy is observed to move towards Y. Explain this observation.
ANSWER
  • Surface tension at X is reduced;
  • Higher surface tension at Y pulls the boat:
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K.C.S.E Physics Q & A - MODEL 2010PP1QN18

19/7/2020

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K.C.S.E Physics Q & A - MODEL 2010PP1QN18

Figure 8 shows a stone of mass 4.0kg immersed in water and suspended from a spring balance with a string. The beaker was placed on a compression balance whose reading was 85N. The density of the stone was 3000kgm-3 while the density of the liquid Was 800kgm-3.
Determine the:

Picture
(a) volume of the liquid displaced; 
(b) Upthrust on the stone; 
(c) reading of the spring balance; 
(d) reading of the compression balance when the stone was removed from the water
answers
Picture
Picture
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K.C.S.E Physics Q & A - MODEL 2009PP1QN17

17/7/2020

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K.C.S.E Physics Q & A - MODEL 2009PP1QN17

(a) State the law of flotation
(b) Figure 10 shows a rectangular metal block of density 10500 kgm-3 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.

Picture

(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 cm3 displaces 10 cm3 of kerosene (density 800 kgm3) when floating. Determine the density of the solid.

answers
Picture
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K.C.S.E Physics Q & A - MODEL 2007PP1QN19

15/7/2020

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K.C.S.E Physics Q & A - MODEL 2007PP1QN19

​ (a) State the law of floating 
(b) Figure 13 shows a simple hydrometer
Picture
​(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.
Picture
​(i) Name the forces 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. 
answers
Picture
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K.C.S.E Physics Q & A - MODEL 2007PP1QN14

15/7/2020

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K.C.S.E Physics Q & A - MODEL 2007PP1QN14

​Figure 8 shows a uniform light bar resting horizontally on corks floating on water in two beakers A and B.
Picture
​Explain why the bar tilts towards side A when equal amount of heat is supplied to each beaker
answer
  • Since the quantity of water A is smaller, heat produces grater change of temperature in A; This causes greater expansion causing the cork of temperature in A; this cause greater expansion causing the cork to sink further.
  • Per unit volume/  greater decrease in density/ lower density in A 
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K.C.S.E Physics Q & A - MODEL 2003PP1QN20

10/7/2020

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K.C.S.E Physics Q & A - MODEL 2003PP1QN20


​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.
Picture
answer
  • Piece of metal does not displace own weight but the two together displace their own weight/ weight of water displaced is less than the weight of metal while weight of water displaced equals the weight of the tow/up thrust equal to combined weight.
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K.C.S.E Physics Q & A - MODEL 2002PP1QN25

10/7/2020

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K.C.S.E Physics Q & A - MODEL 2002PP1QN25


A block of glass of mass 250g floats in mercury. What volume of glass lies under the surface of the mercury? (Density of mercury is 13.6 x 103 kgm-3).

Picture
answer
Picture
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A solid copper sphere will sink in water while a hollow copper sphere of the same mass many float. Explain this observation

5/7/2020

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K.C.S.E Physics Q & A - MODEL 1996PP1QN29

A solid copper sphere will sink in water while a hollow copper sphere of the same mass many float. Explain this observation

Picture
ANSWERS
  • Solid copper is denser than water hence the solid sphere sinks; weight is greater than upthrust. Hollow sphere experiences an upthrust equal to its weight  so it will float/ density of hollow sphere  is less than  that of water
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