The energy of a system as a function of time $t$ is given as $E(t)=A^2 \exp (-\alpha t)$, where $\alpha=0.2 s ^{-1}$. The measurement of $A$ has an error of $1.25 \%$. If the error in the measurement of time is $1.50 \%$, the percentage error in the value of $E(t)$ at $t=5 s$ is
The energy of a system as a function of time $t$ is given as $E(t)=A^2 \exp (-\alpha t)$, where $\alpha=0.2 s ^{-1}$. The measurement of $A$ has an error of $1.25 \%$. If the error in the measurement of time is $1.50 \%$, the percentage error in the value of $E(t)$ at $t=5 s$ is
- [IIT 2015]
- A
$1$
- B
$2$
- C
$3$
- D
$4$
Similar Questions
In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10)\,\,kg\,$ and $(0.10 \pm 0.01)\,\,m\,$ respectively. The error in the measurement of density is
In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10)\,\,kg\,$ and $(0.10 \pm 0.01)\,\,m\,$ respectively. The error in the measurement of density is
- [JEE MAIN 2019]
Explain effect of multiplication or division of error on final result.
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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]
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Two resistance are measured in $Ohm$ and is given as
$R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$ When they are connected in parallel, the percentage error in equivalent resistance is.......... $\%$
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