.. 6.1

Acceleration due to gravity using Rod pendulum
===============================================

**Objective**

Measure the period of oscillations of a rod pendulum using a light
barrier and calculate the value of acceleration due to gravity. Period
of oscillation of a uniform rod about one end is given by
:math:`T = 2\pi\sqrt{2l/3g}`, where :math:`l` is the length and :math:`g` is the acceleration
due to gravity. The pendulum (T-shaped, a knife edge attached to a 6mm
dia rod) is made to swing between an LED and photo-transistor, connected
to expEYES. The LED and photo-transistor are mounted on a U-shaped
bracket as shown in figure.

.. image:: schematics/rod-pendulum.svg
	   :width: 300px
.. image:: pics/light-barrier-photo.jpg
	   :width: 300px

**Procedure**

-  Oscillate the pendulum and click on START
-  Repeat with different pendulum lengths.

**Discussion**

The time period is measured 50 times, using a 14.6cm rod pendulum, and
the average value is 0.627 seconds. The calculated value of ’g’ is
:math:`977,4~cm\cdot s^{-2}`, slightly different from the actual value due to the
following reasons. The length is measured from the knife edge to the
bottom and used in the formula. But there is a small mass projecting
above the knife edge that is not included in the calculation. Another
reason is that the pendulum may not be exactly vertical in the resting
position.
