Physics Paper 3, Nov/Dec 2011  
Questions: 1 2 3 Main
General Comments







Question 1


          The internal diameter, D, of an empty beaker is measured.

          Water is then poured into the beaker until it is about two-thirds full.  The depth, do, of the
          water in the beaker is measured using a graduated scale fixed to the beaker.

          A body of mass, M, supported on the free end of a piece of thread, fixed to the boss of a
          retort stand, is immersed completely in the water as shown in the diagram above.  The
          new depth, d, of the water in the beaker is measured and recorded.

          The procedure is repeated with four different masses.

          Fig 1(a), fig 1(b) and Fig 1(c) show the masses M, the diameter, D, of the beaker and
         depth, d, of water in the beaker respectively.

         (i)     Measure and record the masses, M.
         (ii)    Measure and record the corresponding depth d, where  = 1,2,3,4 and 5.
         (iii)   Also measure and  record D.
         (iv)    Evaluate d – do in each case.
         (v)     Tabulate your readings.
         (vi)    Plot a graph with Mi on the vertical axis and (d – d) on the horizontal axis.
        (vii)    Determine the slope, s, of the graph
       (viii)     Evaluate  K  =     Take p =
       (ix)       State two precaution that are necessary to ensure accurate results when performing
                    this experiment.
   (b)  (i)   Show that the relative density of a substance is equal to the weight of the substance
                divided by the weight of an equal volume of water

        (ii)    The following data were obtained in an experiment

                  mass of empty relative density bottle                                       =  18.5 g
                  mass of relative density bottle filled  with water                    =  65.5 g
                  mass of relative density bottle filled with another liquid  X  =  58.5 g
                 Use the data to determine the relative density of X.



This question was answered by almost all the candidates and the performance was quite
       good.  The masses M were correctly determined however, the depth do and di were
       wrongly measured by almost all the responding candidates because they did not add 2.8 cm
       which happens to be the reference point to their measured values.

       The graph and slope as well as precautions were well handled by candidates.  Part b(i)
       candidates failed to show that the relative density of a substance to be equal to the weight
       of the substance divided by the weight of an equal volume of water.  Part b(ii) was poorly

       Candidates are expected to:

  •  measure and record value of D and do.
  •  read and record five values of M and d to at least 1 d.p.
  • evaluate d-do and record
  • tabulate readings.
  • plot graph of Mi against (d-do) using reasonable scales
  • determine the slope of the graph
  • evaluate K = 
  • state any two of the following precautions.


  •   Read water level at the minimum level of the meniscus of water
  •   Avoid parallax error in reading metre rule/scale balance
  •   Mass not touching the beaker
  •   Note/corrected zero error on metre rule/scale balance
  •   Ensure metre rule is placed vertically
  •   Ensure readings are repeated
  •   Avoid splashing of water from the beaker
  •   Allow the water in the beaker to be still/calm before taking reading.

        The expected answers for part  b are:

        b(i)    Rd  

=   b(i)    Rd     density of substance                                                                                                                                                                                                                                
                          density of water                                                                                                    
              =  mass of substance
                 mass of equal volume of water                                                                                

                  =       mass of substance x acceleration of free fall
                            mass of equal volume of water x acceleration of free fall                                   

                   =       weight of substance
                             weight of equal volume of water                                                                                                               
(ii)     Mass of water  =   68.5  -  18.5  =  47g                                                                                      
          Mass of liquid  =   58.5  -  18.5   =  40g                                                                                      
         Relative density of liquid   =  mass of liquid                                                                             
                                                           mass of equal volume of water
                                                =         40                                                                             
                                                  =  0.85       

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