A students measures the distance traversed in free fall of a body, the initially at rest, in a given time. He uses this data to estimate $g$ , the acceleration due to gravity . If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is
A students measures the distance traversed in free fall of a body, the initially at rest, in a given time. He uses this data to estimate $g$ , the acceleration due to gravity . If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is
- [AIPMT 2010]
- A
$e_2-e_1$
- B
$e_1+2{e_2}$
- C
$e_1+e_2$
- D
$e_1-2{e_2}$
Similar Questions
Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.
They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length $=0.1 \mathrm{~cm}$
Least count for time $=0.1 \mathrm{~s}$
Student
Length of the pendulum $(cm)$
Number of oscillations $(n)$
Total time for $(n)$ oscillations $(s)$
Time period $(s)$
$I.$
$64.0$
$8$
$128.0$
$16.0$
$II.$
$64.0$
$4$
$64.0$
$16.0$
$III.$
$20.0$
$4$
$36.0$
$9.0$
If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,
Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.
They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length $=0.1 \mathrm{~cm}$
Least count for time $=0.1 \mathrm{~s}$
| Student | Length of the pendulum $(cm)$ | Number of oscillations $(n)$ | Total time for $(n)$ oscillations $(s)$ | Time period $(s)$ |
| $I.$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
| $II.$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
| $III.$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,
- [IIT 2008]
Zero error of an instrument introduces
Zero error of an instrument introduces
In an experiment to find acceleration due to gravity $(g)$ using simple pendulum, time period of $0.5\,s$ is measured from time of $100$ oscillation with a watch of $1\;s$ resolution. If measured value of length is $10\; cm$ known to $1\; mm$ accuracy. The accuracy in the determination of $g$ is found to be $x \%$. The value of $x$ is
In an experiment to find acceleration due to gravity $(g)$ using simple pendulum, time period of $0.5\,s$ is measured from time of $100$ oscillation with a watch of $1\;s$ resolution. If measured value of length is $10\; cm$ known to $1\; mm$ accuracy. The accuracy in the determination of $g$ is found to be $x \%$. The value of $x$ is
- [JEE MAIN 2022]
A physical quantity $P$ is given by $P= \frac{{{A^3}{B^{\frac{1}{2}}}}}{{{C^{ - 4}}{D^{\frac{3}{2}}}}}$. The quantity which brings in the maximum percentage error in $P$ is
A physical quantity $P$ is given by $P= \frac{{{A^3}{B^{\frac{1}{2}}}}}{{{C^{ - 4}}{D^{\frac{3}{2}}}}}$. The quantity which brings in the maximum percentage error in $P$ is
In an experiment four quantities $a, b, c$ and $d $ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{{{a^3}{b^2}}}{{cd}}$. $ \%$ error in $P$ is ........ $\%$
In an experiment four quantities $a, b, c$ and $d $ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{{{a^3}{b^2}}}{{cd}}$. $ \%$ error in $P$ is ........ $\%$
- [AIPMT 2013]