314 Higher Engineering Mathematics
2. The pressure p and volume v of a mass of gas
are related by the equation pv =50. If the pressure increases from 25.0 to 25.4, determine the
approximate change in the volume of the gas.
Find also the percentage change in the volume
of the gas.
[−0.032, −1.6%]
3. Determine the approximate increase in (a) the
volume, and (b) the surface area of a cube
of side x cm if x increases from 20.0 cm to
20.05 cm.
[(a) 60 cm 3 (b) 12 cm 2 ]
4. The radius of a sphere decreases from 6.0 cm
to 5.96 cm. Determine the approximate change
in (a) the surface area, and (b) the volume.
[(a) −6.03 cm 2 (b) −18.10 cm 3 ]
5. The rate of flow of a liquid through a
tube is given by Poiseuilles’s equation as:
Q =
pπr 4
8ηL
where Q is the rate of flow, p
is the pressure difference between the ends
of the tube, r is the radius of the tube, L
is the length of the tube and η is the coefficient of viscosity of the liquid. η is obtained
by measuring Q, p, r and L. If Q can be
measured accurate to ±0.5%, p accurate to
±3%, r accurate to ±2% and L accurate to
±1%, calculate the maximum possible percentage error in the value of η.
[12.5%]