8 Consider gas trapped inside an airtight cylinder. For a given
mass of gas kept at a constant temperature, the volume is
inversely proportional to the pressure. When V =10cm^3 ,
the pressure is 40 units. Find:
a the pressure when the volume is 20 cm^3
b the volume when the pressure is 100 units.9 The time taken to complete a certain job varies inversely to the number of workers doing the task. If
20 workers could do the job in 6 days, find how long it would take 15 workers to do the job.10 Consider an object suspended from a spring. The object is dropped so it will
bounce up and down. The time between successive bounces is called theperiod
of the motion. This time varies inversely to the square root of the stiffness of
the spring. The period of a spring of stiffness 100 units is 0 : 2 seconds. Find:
a the period for a spring of stiffness 300 units
b the stiffness required for a 0 : 1 second period.11 The amount of heat received by a body varies
inversely to the square of the distance of the body
from the heat source. If the distance from the
source is decreased by60%, what effect does this
have on the heat received?12 The intensity of light on a screen varies inversely to the square
of the distance between the screen and the light source.
If a screen is illuminated by a light source 20 m away, the
intensity is one fifth of what is required. Where should the
light be placed?The following families of graphs could be useful to help identify variation models:
DIRECT VARIATIONThe graph always passes through
the origin(0,0).INVERSE VARIATION
The graph is always asymptotic to both
thexandy-axes.C VARIATION MODELLING [2.13]
PVOyx312123y kxy kxy kxy kxy kx===== yO xx^2y kx
y kxy k===Variation and power modelling (Chapter 30) 615IGCSE01
cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_30\615IGCSE01_30.CDR Monday, 27 October 2008 2:57:54 PM PETER