Question 85 of 121

A student determined Young's Modulus of elasticity using the formula $Y=\dfrac{Mg{L}^{3}}{4{bd}^{3}\delta }.$ The value of $g$ is taken to be $9.8m{s}^{-2}$ without any significant error, his observations are as following. Physical Quantity Least count of the Equipment used for measurement Observed Value Mass $(M)$ $1g$ $2kg$ Length of bar $(L)$ $1mm$ $1m$ Breadth of bar $(b)$ $0.1mm$ $4cm$ Thickness of bar $(d)$ $0.01mm$ $0.4cm$ Depression $(\delta )$ $0.01mm$ $5mm$ Then the fractional error in the measurement of $Y$ is :