1
a)
Express 5000 rev per minute in radians per second.
[2 Marks]
b)
What is the electrical base unit in the SI system and how is it
defined?
[2 Marks]
c)
A mass is suspended on a spring. The force due to the spring is
given by F = K x. Where x is the displacement.
i) What are the dimensions of K?
[2 marks]
ii) Use the principle of dimensional homogeneity to deduce an
expression for the frequency of oscillation in terms of, the stiffness
(K), the mass, (m) and the gravitational constant, (g).
[4 marks]
EE10142
ANSWER
1 a)
1 rev = 2 pi rad
1 min = 60 sec
5000 rev/min = 5000*2pi/60 = 523.6 rad/sec
b) The SI system uses the Ampere as the base unit. It is defined as the
current that produces a given force between two infinitely long wires
separated by 1 meter.
c) i) F = K . x
Dimension of F is [ML/T/T]
Dimension of x is [L]
Dimension of K (to make equation balance) is
[M/T/T]
ii)
The dimesnions of the quantities are
EE10142
K
[M/T/T]
m
[M]
g
[L/T/T]
frequency [1/T]
we can throw away g because it is the only one with an [L] so
can not be part of a dimensionless number.
A dimensionless number can be formed from
K/m/frequncy/frequency
So we deduce that,
frequency = constant * SQRT(K/m) [Hz]
EE10142