Question

Find the value of x and y using dimensional analysis in the equation of simple pendulum..
T=K.L^x.g^y
where T is time
K is constant
L is length
g is acceleration due to gravity.

Solution needed.....

Answer 1

1.1 International System of System of Units
There are only four fundamental quantities (measurements) necessary to
specify all physical phenomena: length, time, mass and charge. All other quantities are
expressible in terms of these, constructed as a matter of convenience.
The basic system of units used throughout science and technology today is the
internationally accepted Système International (SI) (Table 1). It consists of four base
quantities and their corresponding base units: length (meter), mass (kilogram), time
(second), and electric current (ampere). The unit for electric charge, the coulomb, is
defined in terms of the ampere, and hence is referred to as a derived unit. In addition,
three other quantities, temperature, amount of substance, and luminous intensity are part
of the SI base quantities with corresponding units shown in Table 1.
Mechanics is based on just the first three of these quantities, the MKS or meter-
kilogram-second system. An alternative metric system to this, still widely used, is the so-
called CGS system (centimeter-gram-second). For distance and time measurements,
British Imperial units (especially in the USA) based on the foot (ft), the yard (yd), the
mile (mi), etc., as units of length, and also the minute, hour, day and year as units of time.
Table 1 Système International (SI) System of Units
Base Quantity Base Unit
Length meter (m)
Mass kilogram (kg)
Time second (s)
Electric Current ampere (A)
Temperature Kelvin (K)
Amount of Substance mole (mol)
Luminous Intensity candela (cd)
We shall refer to the dimension of the base quantity by the quantity itself, for example
dim length [length] = L, dim mass [mass] M, dim time [time] T. (1)
1.2 Dimensions of Commonly Encountered Quantities
Many physical quantities are derived from the base quantities by a set of algebraic
relations defining the physical relation between these quantities. The dimension of the