A student determined Young’s Modules of elasticity using the formula \( Y=\dfrac{MgL^{3}}{4bd^{3}\,\delta} \). The value of \( g \) is taken to be \( 9.8 \, \text{m} / \text{s}^{2} \), without any significant error, his observation are as following.
Then the fractional error in the measurement of \( Y \) is:
