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
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]
- A
$0.0083$
- B
$0.0155$
- C
$0.155$
- D
$0.083$
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The radius ( $\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as
$\mathrm{r}=(0.35 \pm 0.05) \mathrm{cm}$
$\mathrm{R}=(100 \pm 10) \mathrm{ohm}$
$l=(15 \pm 0.2) \mathrm{cm}$
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- [JEE MAIN 2024]
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