


1. 

A body is observed to move a distance
s=15m in a time
t=6s. 


The distance was measured using a ruler marked in cm
and the time was measured using a watch giving readings to 0.1s. 

a) 
Express these results correctly. 

b) 
Use the measurements to calculate the speed of the body,
including the uncertainty in the value of the speed. 



2. 

The dimensions of a piece of paper are measured using a ruler
marked in mm. 


The results were x=50mm
and y=40mm. 

a) 
Rewrite the results of these measurements correctly
(that is, giving the right number of significant figures and the
appropriate indeterminacy). 

b) 
Calculate the maximum and minimum values of the area of
the sheet of paper which these measurements give. 

c) 
Express the result of the calculation of area of the sheet of
paper in the form: area = A ±δA. 



3. 

The diameter of a cylindrical piece of metal is measured to a
precision of ±0.01mm. 


The diameter is measured at five different points along the
length of the cylinder. 


The results are shown below; units are mm. 



i) 
6 

ii) 
6.4 

iii) 
5.7 

iv) 
6 

v) 
6.4 


a) 
Rewrite the list of results correctly (that is, giving
the right number of significant figures and the appropriate
indeterminacy). 

b) 
Calculate the average value of the diameter. 

c) 
State the average value of the diameter in a way which gives an
indication of the precision of the manufacturing process used to
make the cylinder. 

d) 
Calculate the average value of the area of cross section of the
cylinder. 


State the result as area=Amm^{2}
±x% 



4. 

The diameter of a metal ball is measured to be 30.0mm
±0.1mm. 


The mass of the ball is measured to be 110g ±1g. 


Use these results to find a value for the density,
ρ of the metal of which the ball is
made. 


Density is defined as mass per unit volume so to calculate the
density of a substance we use the equation: 





Calculate the indeterminacy in this result and state your final
answer in the form: density=ρ±x%. 



5. 

A body which is initially at rest, starts
to move with acceleration a. 


It moves a distance
s=10.00 ±0.01m
in a time t=4.0
±0.1s. 


Calculate the acceleration. 


Now find first the percentage uncertainty in the value
of the acceleration then the absolute uncertainty. 



6. 

A person uses a simple balance to find the mass of a sheet of
paper. 


The balance has a box of known masses of which the smallest is
1g. 


It is found that when 50 identical sheets of paper are on the
balance, 15g is not quite enough for
balance but 16g is just too much. 





Assuming that the balance itself is
perfect and ignoring the indeterminacy in the manufacture
of the masses, state the mass of one sheet of paper including
first an absolute uncertainty and then a
percentage uncertainty. 