Units and Measurements Part 1

The given formula of Young’s modulus of elasticity, $Y=\frac{m g L^{3}}{4 b d^{3} \delta}$ where, Y = Young’s modulus of elasticity, m = mass of the bar, L = length of the bar b = breadth of the bar d = thickness of the bar and $\delta$ = depression of the bar. There is no error in the value of the g. The fractional error in the measurement of Y, $\frac{\Delta Y}{Y}$ $=\frac{\Delta M}{M}+3\frac{\Delta L}{L}+\frac{\Delta b}{b}+3\frac{\Delta d}{d}+\frac{\Delta\delta}{\delta}$ Substituting the values in the above expression, we get $\frac{\Delta Y}{Y}=0.0155$ The fractional error in the measurement of the Young’s modulus is 0.0155.