A physical quantity $P$ is given as $P=\frac{a^2 b^3}{c \sqrt{d}}$ The percentage error in the measurement of $a, b, c$ and $d$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The percentage error in the measurement of quantity $P$ will be $.......\%$
A physical quantity $P$ is given as $P=\frac{a^2 b^3}{c \sqrt{d}}$ The percentage error in the measurement of $a, b, c$ and $d$ are $1 \%, 2 \%, 3 \%$ and $4 \%$ respectively. The percentage error in the measurement of quantity $P$ will be $.......\%$
- [JEE MAIN 2023]
- A
$13$
- B
$14$
- C
$12$
- D
$16$
Similar Questions
A physical quantity $p$ is described by the relation $p\, = a^{1/2}\, b^2\, c^3\, d^{-4}$
If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\% , 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be ........... $\%$
A physical quantity $p$ is described by the relation $p\, = a^{1/2}\, b^2\, c^3\, d^{-4}$
If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\% , 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be ........... $\%$
- [JEE MAIN 2017]
A student performs an experiment for determination of $g \left(=\frac{4 \pi^{2} l }{ T ^{2}}\right), \ell =1 m$ and he commits an error of $\Delta \ell$. For $T$ he takes the time of $n$ oscillations with the stop watch of least count $\Delta T$ and he commits a human error of $0.1 s$ For which of the following data, the measurement of $g$ will be most accurate?
A student performs an experiment for determination of $g \left(=\frac{4 \pi^{2} l }{ T ^{2}}\right), \ell =1 m$ and he commits an error of $\Delta \ell$. For $T$ he takes the time of $n$ oscillations with the stop watch of least count $\Delta T$ and he commits a human error of $0.1 s$ For which of the following data, the measurement of $g$ will be most accurate?
In the expression for time period $T$ of simple pendulum $T=2 \pi \sqrt{\frac{l}{g}}$, if the percentage error in time period $T$ and length $l$ are $2 \%$ and $2 \%$ respectively then percentage error in acceleration due to gravity $g$ is equal to ......... $\%$
In the expression for time period $T$ of simple pendulum $T=2 \pi \sqrt{\frac{l}{g}}$, if the percentage error in time period $T$ and length $l$ are $2 \%$ and $2 \%$ respectively then percentage error in acceleration due to gravity $g$ is equal to ......... $\%$
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]
The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$, respectively. The area of the floor is .................... $m^2$
- [KVPY 2016]