negligible. The gravitational attraction of a body towards the center of the earth resultsin the same acceleration for all bodies at a particular location, irrespective of their mass,shape or material, and this acceleration is called the
acceleration due to gravity
,
g
. Thevalue of
g
varies from place to place, being greatest at the poles and the least at theequator. Because this value is large, bodies fall quickly to the surface of the earth whendropped, and so it is very difficult to measure their acceleration directly with considerableaccuracy.Therefore, the acceleration due to gravity is often determined by indirect methods – for example, using a
simple pendulum
or a
compound pendulum
. If we determine
g
usinga simple pendulum, the result is not very accurate because an ideal simple pendulumcannot be realized under laboratory conditions. Hence, you will use two differentcompound pendulums to determine the acceleration due to gravity in the laboratory,namely the
Bar pendulum
and the
Kater’s pendulum
.
Apparatus
•
Bar Pendulum
•
Small metal wedge
•
Spirit level
•
Telescope
•
Stop watch
•
Meter rod
Theory
A bar pendulum is the simplest form of compound pendulum. It is in the form of arectangular bar (with its length much larger than the breadth and the thickness) with holes(for fixing the knife edges) drilled along its length at equal separation.If a bar pendulum of mass
M
oscillates with a very small amplitude
θ
about a horizontalaxis passing through it, then its angular acceleration (d
2
θ
/d
t
2
) is proportional to theangular displacement
θ
. The motion is
simple harmonic
and the time period
T
is given by