$A$ 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 observations are as follows:
Physical Quantity Least count and Observed value Mass $(M)$ $1 \, g$ and $2 \, kg$ Length of bar $(L)$ $1 \, mm$ and $1 \, m$ Breadth of bar $(b)$ $0.1 \, mm$ and $4 \, cm$ Thickness of bar $(d)$ $0.01 \, mm$ and $0.4 \, cm$ Depression $(\delta)$ $0.01 \, mm$ and $5 \, mm$
Then the fractional error in the measurement of $Y$ is:
| Physical Quantity | Least count and Observed value |
| Mass $(M)$ | $1 \, g$ and $2 \, kg$ |
| Length of bar $(L)$ | $1 \, mm$ and $1 \, m$ |
| Breadth of bar $(b)$ | $0.1 \, mm$ and $4 \, cm$ |
| Thickness of bar $(d)$ | $0.01 \, mm$ and $0.4 \, cm$ |
| Depression $(\delta)$ | $0.01 \, mm$ and $5 \, mm$ |
Then the fractional error in the measurement of $Y$ is:
- A$0.0083$
- B$0.0155$
- C$0.155$
- D$0.083$
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