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Determination of the Young modulus of a metal bar in the form of a cantileveris an old experimental concept. However, we have taken the advantage of modernadvanced technology of smartphone camera to find the load depression graph ofthe cantilever by taking photographs with the smartphone camera. Smartphonephotography allows us to find a precise transverse magnification of an objectfrom the size of the real image formed on the sensor of the camera. Image sizeon the sensor can be obtained with micron level accuracy. From the loaddepression graph, we have determined the Young modulus of the bar. Thesensitive measurements of the depression of the cantilever at its free end byits own weight, have allowed us to determine the density of aluminium. We haveadded an analysis of the chi squred minimisation technique for determining theparameters and their uncertainities in a linear fit. Starting from thecurvature matrix we have made a comprehensive analysis of the error matrixrelevant for a two parameter linear fit. Then we have shown how to form theerror matrix for the fitted parameters which includes the covariance termbetween the two correlated parameters, in the context of our specificexperiment. We have propagated the errors in the parameters to find theuncertainties in the Young modulus and the density of the bar. We have shownthat a precise measurement is possible by smartphone photography.

Estimation of the error matrix in a linear least square fit to the data from an experiment performed by smartphone photography