  Determination of the Young modulus of a metal bar in the form of a cantilever
is an old experimental concept. However, we have taken the advantage of modern
advanced technology of smartphone camera to find the load depression graph of
the cantilever by taking photographs with the smartphone camera. Smartphone
photography allows us to find a precise transverse magnification of an object
from the size of the real image formed on the sensor of the camera. Image size
on the sensor can be obtained with micron level accuracy. From the load
depression graph, we have determined the Young modulus of the bar. The
sensitive measurements of the depression of the cantilever at its free end by
its own weight, have allowed us to determine the density of aluminium. We have
added an analysis of the chi squred minimisation technique for determining the
parameters and their uncertainities in a linear fit. Starting from the
curvature matrix we have made a comprehensive analysis of the error matrix
relevant for a two parameter linear fit. Then we have shown how to form the
error matrix for the fitted parameters which includes the covariance term
between the two correlated parameters, in the context of our specific
experiment. We have propagated the errors in the parameters to find the
uncertainties in the Young modulus and the density of the bar. We have shown
that a precise measurement is possible by smartphone photography.
