A student determined Young's Modulus of elasticity using the formula $Y=\frac{M g L^{3}}{4 b d^{3} \delta} .$ The value of $g$ is taken to be $9.8 \,{m} / {s}^{2}$, without any significant error, his observation are as following.
| Physical Quantity | Least count of the Equipment used for measurement | Observed value |
| Mass $({M})$ | $1\; {g}$ | $2\; {kg}$ |
| Length of bar $(L)$ | $1\; {mm}$ | $1 \;{m}$ |
| Breadth of bar $(b)$ | $0.1\; {mm}$ | $4\; {cm}$ |
| Thickness of bar $(d)$ | $0.01\; {mm}$ | $0.4 \;{cm}$ |
| Depression $(\delta)$ | $0.01\; {mm}$ | $5 \;{mm}$ |
Then the fractional error in the measurement of ${Y}$ is
JEE MAIN 2021, Diffcult
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